{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "`ftol` termination condition is satisfied.\n",
      "Function evaluations 15, initial cost 6.4347e-01, final cost 2.3075e-09, first-order optimality 1.81e-07.\n"
     ]
    },
    {
     "data": {
      "image/png": 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0v9nb2+Of//wnZs2aBVdXVwQEBGDZsmXIzs7GlClTqvFPj4iIiIjqtIQEMT3u9m2lyIFTairw++9K0PTWW8DOnWW/Vnq62FEOAMLCgKwswNsb8PHRffT21v3t99y5Nfb2iIiqC0MpqjHTp09Hs2bNsHz5cgwfPhw5OTkICgrCoEGDEBkZqfc5ISEhsLOzw6uvvopbt27B2toaTZs2xWeffYZx48YBABo2bIjdu3dj1qxZCA0NhaurK6ZMmYI33nijzL6sWLECkyZNwuOPPw5fX1+sXr0ap0+f1ly3sLDAmjVrsHjxYrz11lvo3r07fv3111Kv85///AfFxcUYN24cMjIyEBYWhr1798LFxeXR/rCIiIiIqHYrLha7zMkh0507ynFyshjBJAdNL79c/tS5Bw8AeefmNm1EYFUyYJKPtYOmN94QhYjIRKikkgvtUKWp1Wo4OTkhPT0djo6OOtdyc3MRFxeH4OBg7rxGdRr/LhMREZHJysnRDZnkkU3LlytB09NPA19/XfZrpKSIhb4BYNYsMfqpYUNRfH1F8fERpVs33XWaiIhMTHk5iTaOlCIiIiIiItOVlQXcugXEx4tpdZMmKUFTZCTw+efA/fv6nztvHuDuLo69vcWjp6cSNsmBU8OGVV8MnIioHmMoRUREREREdVNBgRjhFBCgBE2ffAL88IMSRD14oPucIUOUoKmwUAmkbG11w6aGDZXXBMQi4ytWAH9vkENERI+OoRQREREREdVux48DJ04oQdOtW6IkJoq1npKTxe5ygNjN7scfdZ/v6CiCK39/MVVPFhkJvPiiGO3k7KwbQpXUoEG1vy0iovqOoRQRERERERleVhbw119KyFTyMSZGGdG0bRuwZo3+17G0FLvayaHUqFFAq1ZKCOXvD5TYVVkjKKja3xYREVUcQykiIiIiIqp+WVnAzZu65Y03lIBo3jzgww/Lfv6tW0oo1bWrMk1PDprkY09PwMxMed5jj4lCRES1HkMpIiIiIiKqPHmkU+PGyiLfmzYBH38sAqh790o/Z8wYoEMHcRwUJAIqOVzSfgwIAJo21X3emDE1/Y6IiMjAGEoREREREVHZ/vwTOHSo9KgnOXQ6cwZo314cP3gAnDypPNfZWYRPctHeFnzmTLGmExER1VsMpYiIiIiI6qO8PBEu3bgBxMXpBk6bNgGtW4t2e/YAs2bpfw1nZ2X3OkDsbNekiQigAgPF9bJoT7kjIqJ6iaEUGV1QUBBmzpyJmTNnVvk1fv31V/Ts2RMPHjyAc3lffiro5s2bCA4ORmxsLNq1a/fIr1eWiRMnIi0tDd99990jvc7ChQvx3Xff4ezZs9XSLyIiIjIR9++L0On6daBHD8DbW9SvWwe89BIgSfqfd/WqEkq1bw8MG6Y74qms0KlpU91pd0REROVgKEXlOnbsGLp3744+ffpgz549xu4OAOCJJ55Au3btsGrVKk1deHg4EhMT4VTWzio14MaNG5g/fz4OHjyI+/fvw93dHR07dsT777+PZs2a1dh9VSoVdu7ciWHDhmnqXnvtNbz88ss1dk8iIiKqA37/XexSJ4dQN24AaWnK9Z07RbgEAF5eIpCytwcaNQKCg0WRA6du3ZTnPfmkKERERNWMoRSVa9OmTXj55Zfx2WefIT4+HgEBAcbukl5WVlbwln/zZwD5+fno06cPWrRogW+//RY+Pj5ISEjA7t27kZ6ebrB+yBwcHODg4GDw+xIREZEBZGaK6XVy0KT9uHIlMHCgaHflCvDee6Wf7+2tuxg5ADz1FJCUJHauU6kM8z6IiIhKMMmJ3OvWrUNwcDBsbGzQsWNHHD58uNz2W7duRWhoKOzs7ODj44NJkyYhNTXVQL2tvbKysvB///d/+Oc//4lBgwZh8+bNOtd//fVXqFQq7N+/H2FhYbCzs0N4eDguX76saXP9+nUMHToUXl5ecHBwQKdOnbBv374y7zl58mQMGjRIp66wsBDe3t7YtGkTJk6ciIMHD2L16tVQqVRQqVS4efOmpi9pWr8NPHr0KHr06AE7Ozu4uLigX79+ePDgAQBgz549eOyxx+Ds7Aw3NzcMGjQI169fr/CfzYULF3Djxg2sW7cOXbt2RWBgICIiIvDOO++gU6dOmnbnzp1Dr169YGtrCzc3N7zwwgvIzMws83WDgoJ0RoABQLt27bBw4ULNdQAYPnw4VCqV5nzhwoU60wyLi4uxePFi+Pn5wdraGu3atdMZ6Xbz5k2oVCp8++236NmzJ+zs7BAaGoqYmJgK/xkQERFRNZEkERAdPQps2QJcuqRc27kTaNAAaNsWGD4cePVVMfVuzx4xxe7KFaVtu3bAv/4FfPAB8P33wLlzItBKTASOHAH691fa2tuL0VIMpIiIyIhMLpTavn07Zs6cifnz5yM2Nhbdu3dH//79ER8fr7f9kSNHMH78eEyZMgXnz5/Hjh07cPLkSTz//PMG7nnts337djRv3hzNmzfHc889h6ioKEh61h2YP38+VqxYgVOnTsHCwgKTJ0/WXMvMzMSAAQOwb98+xMbGol+/fhg8eHCZn8fzzz+PPXv2IDExUVO3e/duZGZmYtSoUVi9ejW6deuGqVOnIjExEYmJifD39y/1OmfPnsWTTz6JVq1aISYmBkeOHMHgwYNRVFQEQARukZGROHnyJPbv3w8zMzMMHz4cxcXFFfqz8fDwgJmZGb7++mvNa5aUnZ2Np556Ci4uLjh58iR27NiBffv24aWXXqrQPfQ5+fduNlFRUUhMTNScl7R69WqsWLECy5cvxx9//IF+/fphyJAhuHr1qk67+fPn47XXXsPZs2fRrFkzjBkzBoWFhVXuHxEREVXAjRvAm28CzzwDdOgAODkBPj7AY48BEyYAe/cqbeXvOa6uQKdOwOjRwOuvA599Bhw4AIwbp7Rt2hRYuxZ45RWx4Hjr1iJ8IiIiqq0kE9O5c2dp2rRpOnUtWrSQ5s6dq7f9+++/LzVq1Einbs2aNZKfn1+F75meni4BkNLT00tdy8nJkS5cuCDl5OToXsjMLLtUpm12dsXaVkF4eLi0atUqSZIkqaCgQHJ3d5eio6M11w8cOCABkPbt26ep++mnnyQApd+vlpCQEOnDDz/UnAcGBkorV67Uuf7ee+9pzocNGyZNnDhRc96jRw/p3//+t85ryn158OCBJEmSNGbMGCkiIqLC7zU5OVkCIJ07d06SJEmKi4uTAEixsbFlPmft2rWSnZ2d1KBBA6lnz57S4sWLpevXr2uuf/LJJ5KLi4uUqfXn/9NPP0lmZmZSUlKSJEmSNGHCBGno0KGa6yX/LCRJkkJDQ6UFCxZozgFIO3fu1GmzYMECKTQ0VHPu6+srvfPOOzptOnXqJE2fPl3n/X322Wea6+fPn5cASBcvXtT7fsv8u0xERESK+/cl6cQJSfriC0lasECSxo6VpE6dJGnjRqXN8eOSJMZHKcXMTJICAyWpVy9J2rZNaZufL0l/f78hIiKqK8rLSbSZ1Eip/Px8nD59Gn379tWp79u3L44dO6b3OeHh4Zq1gCRJwt27d/H1119joDw3v6Y4OJRdRozQbevpWXZb7WHYgFiYUl+7Srp8+TJ+++03PPPMMwAACwsLjB49Gps2bSrVtm3btppjHx8fAEBycjIAMSJp9uzZCAkJgbOzMxwcHHDp0qUyR0oBYrRUVFSU5nV++uknndFXFSGPlCrL9evXMXbsWDRq1AiOjo4IDg4GgHL7VdK//vUvJCUl4YsvvkC3bt2wY8cOtGrVCtHR0QCAixcvIjQ0FPZav6GMiIhAcXGxzhTH6qZWq3Hnzh1ERETo1EdERODixYs6deV9dkRERFSGjAzgzBmxppPs3DnAw0OMaOrSBXjuOWDRIuDLL4GTJ8Ui5LLmzYEXXwSWLxfT7C5cALKzgZs3gf37xQgqmaVl6R3uiIiITIRJLXSekpKCoqIieHl56dR7eXkhKSlJ73PCw8OxdetWjB49Grm5uSgsLMSQIUPw4YcflnmfvLw85OXlac7VanX1vIFaZOPGjSgsLETDhg01dZIkwdLSEg8ePICLi4um3tLSUnOs+ntdAnka3KxZs7B3714sX74cTZo0ga2tLUaOHIn8/Pwy7z1+/HjMnTsXMTExiImJQVBQELp3716p/tva2pZ7ffDgwfD398enn34KX19fFBcXo3Xr1uX2S58GDRpgyJAhGDJkCJYsWYJ+/fphyZIl6NOnDyRJ0vx5lFRWvZmZWakpkgUFBZXqU1n30Nef8j47IiKiei8rC/jf/8TaTdrl7l1x/ZVXxPpNgFhMPCVFHPv4iKl02kVr7Uc4OwMff2zId0JERFQrmVQoJavID+OyCxcuYMaMGXjrrbfQr18/JCYmYtasWZg2bRo2btyo9zlLly7FokWLHq2T5Sx2DXNz3fPyRq6YlRjsdvNmlbskKywsxJYtW7BixYpSo85GjBiBrVu3VnhdpMOHD2PixIkYPnw4ALHG1M2H9NHNzQ3Dhg1DVFQUYmJiMGnSJJ3rVlZWZa7jJGvbti3279+v93NKTU3FxYsXsWHDBk3YdeTIkQq9n/KoVCq0aNFCMyovJCQEn3/+ObKysjSjpY4ePQozMzM0a9ZM72t4eHjorKelVqsRFxen08bS0rLc9+/o6AhfX18cOXIEjz/+uKb+2LFj6Ny5c5XfHxERkckpKhLfnS5fFouLX74MdOwIvPCCuJ6ZCTz9tP7nengAFlpfpd3dgdhYsctdgwY13nUiIiJTYFKhlLu7O8zNzUuNikpOTi41ekq2dOlSREREYNasWQBEmGFvb4/u3btjyZIlmilN2ubNm4fIyEjNuVqt1rvYdrkqs+hkTbUtw48//ogHDx5gypQpcHJy0rk2cuRIbNy4scKhVJMmTfDtt99i8ODBUKlUePPNNys0Euf555/HoEGDUFRUhAkTJuhcCwoKwokTJ3Dz5k04ODjA1dW11PPnzZuHNm3aYPr06Zg2bRqsrKxw4MABPP3003B1dYWbmxs++eQT+Pj4ID4+HnPnzq3Q+5GdPXsWCxYswLhx4xASEgIrKyscPHgQmzZtwpw5cwAAzz77LBYsWIAJEyZg4cKFuHfvHl5++WWMGzeuzL+PvXr1wubNmzF48GC4uLjgzTffhHmJkDIoKAj79+9HREQErK2tdUatyWbNmoUFCxagcePGaNeuHaKionD27Fls3bq1Uu+TiIjIJBQWKgFSZiYwcaIIoa5eBUqOkh46VAmlPD2Bnj2Bhg1Lj3wq8R0JKpXuaCgiIiJ6KJMKpaysrNCxY0dER0drRuYAQHR0NIYOHar3OdnZ2bCw0P1jkEOAktOoZNbW1rC2tq6mXtc+GzduRO/evUsFUoAYKfXuu+/izJkzFXqtlStXYvLkyQgPD4e7uzvmzJlToemOvXv3ho+PD1q1agVfX1+da6+99homTJiAkJAQ5OTklBpJBADNmjXDzz//jNdffx2dO3eGra0tunTpgjFjxsDMzAxfffUVZsyYgdatW6N58+ZYs2YNnnjiiQq9JwDw8/NDUFAQFi1ahJs3b0KlUmnOX3nlFQCAnZ0d9u7di3//+9/o1KkT7OzsMGLECHwgD/PXY968ebhx4wYGDRoEJycnvP3226Xe34oVKxAZGYlPP/0UDRs21DvybMaMGVCr1Xj11VeRnJyMkJAQ7Nq1C02bNq3weyQiIqpTiouBv/7SHfV06ZIoERHA11+LdnZ2YkpedrY4t7EBmjUT6zw1bw5ojypWqYBffjH8eyEiIqonVFJZyUsdtX37dowbNw4ff/wxunXrhk8++QSffvopzp8/j8DAQMybNw+3b9/Gli1bAACbN2/G1KlTsWbNGs30vZkzZ8LMzAwnTpyo0D3VajWcnJyQnp4OR0dHnWu5ubmIi4tDcHAwbGxsqv39mqrs7Gz4+vpi06ZN+Mc//mHs7hD4d5mIiGqJjAzgyhUgJwd47DFRV1wMuLkBaWn6n9OqFfDnn8r5F1+I6XYtWgABAaWXQyAiIqJHUl5Oos2kRkoBwOjRo5GamorFixcjMTERrVu3xu7duxEYGAgASExM1NlhbeLEicjIyMDatWvx6quvwtnZGb169cJ7771nrLdQrxUXFyMpKQkrVqyAk5MThgwZYuwuERERkbHs3w+cP687+un2bXGtXTuxhhMgQiV/fzH6qWlTETY1by4eW7QQI6G0PfecQd8GERER6WdyI6WMgSOlqs/NmzcRHBwMPz8/bN68GU8++aSxu0R/499lIiKqdvn5wLVrwIULwMWLQG4u8M47yvWWLUUYVZKnJ9Chg5iGJ0tOFqOlSm4YQ0RERAZXb0dKUd0WFBRU5lpeREREZAI+/BA4dEiMgLp6VSxCLmvQAFiyRKzlBAB9+4pgSh71JK/7pGeTD3h6Gqb/REREVG0YShERERFR9cjOFiObLlxQSmIioL1O5969wE8/KecODkBIiFIKCwFLS3Ft9WrD9p+IiIgMiqEUEREREVVOZqYIk2Rvvgls3QrcvAnoG/F87x7g4SGOJ04EnnxSCaH8/JSRUURERFSvMJQyEE5Jo7qOf4eJiOqhBw90Rz3JJSFB7HTn5CTaqdVAXJw49vDQHfnUsqWYlicbOdLgb4OIiIhqJ4ZSNczy7+Hn2dnZsLW1NXJviKouOzsbgPJ3moiITMiDB8CffwKdOwPW1qJu1ixg+fKyn3P5smgPAC++CIwYIQIoeUQUERER0UMwlKph5ubmcHZ2RnJyMgDAzs4OKg5RpzpEkiRkZ2cjOTkZzs7OMOeuRkREdVd2thjp9Oefopw7Jx7v3BHXT58Wu9oBQECA8iiPeNIe/aS92HhIiGHfBxEREZkEhlIG4O3tDQCaYIqoLnJ2dtb8XSYiolquoAC4ckUETj16APL/vz/6CJg9W/9zAgKA+/eV84kTRdGeekdERERUjRhKGYBKpYKPjw88PT1RUFBg7O4QVZqlpSVHSBER1VapqcCxY8qopz//FDvgyd85tm8HRo0Sx23aAO7u4rF1a+UxJERZH0rGMIqIiIhqGEMpAzI3N+cP9kRERFR5kgTcvatMuXviCaB9e3Ht0CHgH/8o/RwHBxE4WVkpdf36iZ3wiIiIiGoBhlJEREREtU1yMrBzp+66T6mpyvV33lFCqTZtgNBQEUDJpU0bMR2v5DqWXNeSiIiIahGGUkRERETGUFgIXLsG/PEH8PvvQJcuwJAh4trdu8C0abrtVSqgSRMRODVrptQ3aQKcPWuwbhMRERFVF4ZSRERERIaQkQFs2qSEUOfPA7m5yvVJk5RQqnlzoH9/oFUrZd2nli0BW1vj9J2IiIioBjCUIiIiIqouhYVi1zs5eAoMVEY8qVTAK6+I9aFk9vYidGrbFujTR6m3sgJ27zZs34mIiIgMjKEUERERUVUVFwOrV4sQ6o8/xOinvDzlevfuSijl4AC88ALg5SVCqNBQoFEjwMzMOH0nIiIiMjKGUkRERETlKSgALl8WI5/++AOwtASWLBHXzMyA5cuBO3eU9g4OyuLjXbvqvtbHHxuu30RERES1HEMpIiIiopI2bACOHRNB1IULIpiS+fgooRQA/POfQFGRMvopKIijn4iIiIgqgKEUERER1T/FxUBcnNi1LjZW7Hb36afK9S+/BA4dUs4bNFBCp7ZtxfPl4OmNNwzadSIiIiJTwVCKiIiI6ocffgCio0UQdfas2A1P2wcfiPAJACZMAHr3FgFU27Zi9JNKZeAOExEREZk2hlJERERkOtLTldDp99/FGk5WVuLazp1AVJTS1toaaN0aaN8eaNdOd1e8yZMN2GkiIiKi+omhFBEREdVdp08Du3cr0/Di4nSv//vfYsodAAwZAri4iACqfXugeXOxaDkRERERGYVJrsK5bt06BAcHw8bGBh07dsThw4fLbZ+Xl4f58+cjMDAQ1tbWaNy4MTZt2mSg3hIREVG5CguB8+eBrVuBWbOAhATl2s8/A2+9BXz7rRJIBQYCQ4cCCxaIEEo2bBiwYgUwbpwYIcVAioiIiMioTG6k1Pbt2zFz5kysW7cOERER2LBhA/r3748LFy4gICBA73NGjRqFu3fvYuPGjWjSpAmSk5NRWFho4J4TERERAOCvv3RHP507B+TmKte7dgX8/MTx44+LkEke/RQaCri6GqPXRERERFRJKknSXkCh7uvSpQs6dOiA9evXa+patmyJYcOGYenSpaXa79mzB8888wxu3LgB1yp+iVWr1XByckJ6ejocHR2r3HciIqJ6JSNDBE+nTwNPPgm0aSPq/+//gNGjdds6OIjAqV07YOJEICzMwJ0lIiIiooqqaE5iUiOl8vPzcfr0acydO1envm/fvjh27Jje5+zatQthYWFYtmwZ/vvf/8Le3h5DhgzB22+/DVtbW0N0m4iIyPRlZwMnTogA6swZ8Xj1qrK4+H/+o4RSYWHAU08pC5C3bw80bgyYmeSqA0RERET1lkmFUikpKSgqKoKXl5dOvZeXF5KSkvQ+58aNGzhy5AhsbGywc+dOpKSkYPr06bh//36Z60rl5eUhLy9Pc65Wq6vvTRAREdV1KSkieHJ3Bzp0EHWXLgG9epVu6+8v2jRpotQ1agT873+G6SsRERERGY1JhVIylUqlcy5JUqk6WXFxMVQqFbZu3QonJycAwAcffICRI0fio48+0jtaaunSpVi0aFH1d5yIiKiuSUpSRj/JI6Bu3RLXnn8e+PRTcdy6NdCsmRgN1bGjCKLatwc8PY3XdyIiIiIyKpMKpdzd3WFubl5qVFRycnKp0VMyHx8fNGzYUBNIAWINKkmSkJCQgKZNm5Z6zrx58xAZGak5V6vV8Pf3r6Z3QUREVAtJktj1Tq0GWrUSdenpgI+P/vbNmgHa//ZaWQGXL9d8P4mIiIiozjCpUMrKygodO3ZEdHQ0hg8frqmPjo7G0KFD9T4nIiICO3bsQGZmJhwcHAAAV65cgZmZGfzknX1KsLa2hrW1dfW/ASIiotpAkoCbN3VHQJ05A9y7BzzxBHDggGjn5CTCJwsLMfJJHgHVrh3AjT+IiIiI6CFMKpQCgMjISIwbNw5hYWHo1q0bPvnkE8THx2PatGkAxCin27dvY8uWLQCAsWPH4u2338akSZOwaNEipKSkYNasWZg8eTIXOiciItMnScD9+4Cbm1LXogVw5UrptubmQFGRbt2ffwKWljXbRyIiIiIySSYXSo0ePRqpqalYvHgxEhMT0bp1a+zevRuBgYEAgMTERMTHx2vaOzg4IDo6Gi+//DLCwsLg5uaGUaNGYcmSJcZ6C0RERDXnzh3g1CndYmMDaP3biEaNxEipNm3EyCe5tGkDlPyFDQMpIiIiIqoilSTJezFTVanVajg5OSE9PR2OnK5ARES10Zw5wH//CyQmlr5mYQHcvQu4uorzpCRxbGVl2D4SERERkUmoaE5iciOliIiI6qX798UaUPLop9hYMbXOzk5cz84WgZSZmVioPCxMKW3bitFSMm9v47wHIiIiIqpXGEoRERHVVT/9BGzZIkKoGzdKXz97FggPF8f//CcwZgwQGgrY2xu0m0RERERE+jCUIiIiqs0yM0W4dPKkCJ8WLgSaNhXXrl4F/u//lLaNG4uRT506icd27ZRrISEG7DQRERER0cMxlCIiIqpNbt0CfvgB+O03EUJdvAgUFyvXn3pKCaX69gWWLhUBVMeOgIuLcfpMRERERFQFDKWIiIiMobgYuHJFjIBq107sbAeIUVH/+pdu24YNlfWfOnRQ6kNCOAKKiIiIiOoshlJERESGcPu2GP30228iiDp5ElCrxbW33lJCqc6dxWiozp2VIMrHx3j9JiIiIiKqIQyliIiIqtuDB2ItKH9/cX7pEtCyZel2trZi5JOfn1Ln5QX873+G6ScRERERkRHVWCh19+5dvPbaa9i/fz+Sk5MhSZLO9aKiopq6NRERkeHk5oopd9qjoK5cAZ59FvjiC9GmaVPA2RkIDBSLkHfuLEqrVoAFfz9ERERERPVTjX0TnjhxIuLj4/Hmm2/Cx8cHKpWqpm5FRERkeEVFQLduQGwsUFhY+vrdu8qxubk4t7IyXP+IiIiIiGq5Gguljhw5gsOHD6Od9nbUREREdYUkiZ3wTpwQo59++w2wtASio8V1c3MgL08EUp6eYuSTPAoqLAxwd9d9PQZSREREREQ6aiyU8vf3LzVlj4iIqNb7+GNgzx4RRiUl6V6ztgby85WAadMmET4FBAAcEUxEREREVCk1FkqtWrUKc+fOxYYNGxAUFFRTtyEiIqq8oiLg/HkRPJ07B6xerYRKP/8MfP+9OLawANq2Bbp0UUZBaa8B1bGj4ftORERERGQiVFINDWdycXFBdnY2CgsLYWdnB0tLS53r9+/fr4nbGoVarYaTkxPS09Ph6Oho7O4QEVFJSUnAsWMihDpxAjh1CsjKUq7fuAEEB4vjXbuAa9dEENWhg9ghj4iIiIiIKqyiOUmNjpQiIiIyuKws4PRpMYrJ3l7UrVgBLF+u265BAzH6qUsX3fWehgwxXF+JiIiIiOqxGgulJkyYUFMvTUREJBQXA5cuidFPx4+Lxz//FNPzoqOB3r1Fu/BwZRpe167isUULsVg5EREREREZRY2FUgBQVFSE7777DhcvXoRKpUJISAiGDBkCc/4QQEREVSFJytpPu3YB48YBanXpdg0bAmlpyvnw4aIQEREREVGtUWOh1LVr1zBgwADcvn0bzZs3hyRJuHLlCvz9/fHTTz+hcePGNXVrIiIyBfn5wNmzYgRUTIx4nDsXePFFcd3fXwRSdnZAWJjuKKiGDY3adSIiIiIiergaW+h8wIABkCQJW7duhaurKwAgNTUVzz33HMzMzPDTTz/VxG2NggudExFVk+RkYNkyEUKdPg3k5elenzQJ2LRJHBcWih30WrXS3RGPiIiIiIiMqqI5SY2FUvb29jh+/DjatGmjU//7778jIiICmZmZNXFbo2AoRURUSbm5wJkzYvSTtzcwdqyoT0sDXFyUdm5uYvRT165At25iRJSTk1G6TEREREREFWP03fesra2RkZFRqj4zMxNW2rscERGRaZMk4K+/dKfhxcYCBQXi+uOPK6GUszOwYAHQuLEIopo0UdaQIiIiIiIik2JWUy88aNAgvPDCCzhx4gQkSYIkSTh+/DimTZuGITW83fa6desQHBwMGxsbdOzYEYcPH67Q844ePQoLCwu0a9euRvtHRGTSsrOBixd168LCgDFjgDVrgN9+E4GUpycwdCjwj3/otl24UCxg3rQpAykiIiIiIhNWYyOl1qxZgwkTJqBbt26wtLQEABQWFmLIkCFYvXp1Td0W27dvx8yZM7Fu3TpERERgw4YN6N+/Py5cuICAgIAyn5eeno7x48fjySefxN27d2usf0REJkWSgBs3lBFQMTHA778DPj7ArVuijUolRkPduiWm4MlT8YKCGDoREREREdVjNbamlOzq1au4dOkSJElCSEgImjRpUpO3Q5cuXdChQwesX79eU9eyZUsMGzYMS5cuLfN5zzzzDJo2bQpzc3N89913OHv2bIXvyTWliKhemj0b2LwZuHev9DUfH7EIubw+lCQxgCIiIiIiqieMvqaUrGnTpmjatGlN3wYAkJ+fj9OnT2Pu3Lk69X379sWxY8fKfF5UVBSuX7+OL774AkuWLKnpbhIR1Q3yWlDHjokRUCdOAL/+CtjZiet5eSKQsrICOnbUXZDcz083hGIgRUREREREJVRrKBUZGYm3334b9vb2iIyMLLftBx98UJ23BgCkpKSgqKgIXl5eOvVeXl5ISkrS+5yrV69i7ty5OHz4MCwquKV4Xl4e8rS2KVer1VXvNBFRbXLpEvDTTyKIOnYMKPn/zlOnxFQ8AJg+XSxQ3q4dYG1t8K4SEREREVHdVq2hVGxsLAr+3k0pNja2Ol+6UlQlfiMvSVKpOgAoKirC2LFjsWjRIjRr1qzCr7906VIsWrTokftJRGRUd+6I4CkiQky3A4C9e4HXXlPaWFoC7dsD4eFiBFTr1sq15s0N218iIiIiIjIpNb6mlCHl5+fDzs4OO3bswPDhwzX1//73v3H27FkcPHhQp31aWhpcXFxgbm6uqSsuLoYkSTA3N8fPP/+MXr16lbqPvpFS/v7+XFOKiGqvggKxALk8Fe/YMSA+XlyLigImThTHZ88CixaJACo8XEzLs7U1Vq+JiIiIiKgOMvqaUpMnT8bq1avRoEEDnfqsrCy8/PLL2LRpU7Xf08rKCh07dkR0dLROKBUdHY2hQ4eWau/o6Ihz587p1K1btw6//PILvv76awQHB+u9j7W1Naw5VYWIarPiYsDMTBwfPQr06QPk5Oi2MTMD2rYVa0LJ2rUDdu40WDeJiIiIiKj+qrGRUubm5khMTISnp6dOfUpKCry9vVFYWFgTt8X27dsxbtw4fPzxx+jWrRs++eQTfPrppzh//jwCAwMxb9483L59G1u2bNH7/IULF3L3PSKqW4qKgAsXlHWgjh0Taz3J04zv3QM8PcVOePIIqG7dgM6dAQcH4/adiIiIiIhMjtFGSqnVakiSBEmSkJGRARsbG821oqIi7N69u1RQVZ1Gjx6N1NRULF68GImJiWjdujV2796NwMBAAEBiYiLi5SkrRER1VXY2sHy5Mh2v5IYLR48qxx4ewNWrQKNGyugpIiIiIiIiI6v2kVJmZmZ6FxXX3FClwqJFizB//vzqvK1RcaQUEdWo+HgRMhUUAOPHi7riYjHySQ6j7O2BLl3EouXduoljV1fj9ZmIiIiIiOoto42UOnDgACRJQq9evfDNN9/AVeuHIisrKwQGBsLX17e6b0tEZBq0FyQ/elQ8JiSIa40aKaGUmRnw+uti+l14ONCmDWBRY8sEEhERERERVbtq/wmmR48eAIC4uDgEBASUO2qKiKjey8zUXdepe3fgxAndNubmQPv2InwqLFTCpzlzDNdPIiIiIiKialatodQff/yB1q1bw8zMDOnp6aV2ttPWtm3b6rw1EVHtJ0nAtWvKCKijR4EbN4C0NEDe0bNDB+DyZRFAhYeL6XidOonpeURERERERCakWteUMjMzQ1JSEjw9PTVrS+l7eZVKhaKiouq6rdFxTSkiKtf33wNRUSKIunev9PWTJ4GwMHGcmQnY2XFBciIiIiIiqrOMsqZUXFwcPDw8NMdERPVKaqoyAuqllwA/P1F/5YoIpgAxIiosTBkFFR4udseTaU/lIyIiIiIiMmHVGkoFBgbqPSYiMjmSBFy/LgKoo0eBI0eAixeV623aAM8+K44HDgRUKhFCdeigTNUjIiIiIiKqx2psq6bPP/8c7u7uGDhwIABg9uzZ+OSTTxASEoJt27YxtCKiuqWgAMjLU0Yyff89MHx46XYtWojwKThYqQsJEYWIiIiIiIg0amzRknfffRe2trYAgJiYGKxduxbLli2Du7s7XnnllZq6LRFR9UhPB/bsAd54A+jZE3ByAlatUq536QJYWYkAavZsEVLduydGS332mZiWR0RERERERGWqsZFSt27dQpMmTQAA3333HUaOHIkXXngBEREReOKJJ2rqtkREVZeWBrz+upiK9+efYoqetthY5djHB1CrORWPiIiIiIioimoslHJwcEBqaioCAgLw888/a0ZH2djYICcnp6ZuS0T0cEVFwB9/iPDJygp48UVR7+AAbNkCZGWJ88aNgcceE6OhHnsMaN5c93UYSBEREREREVVZjYVSffr0wfPPP4/27dvjypUrmrWlzp8/j6CgoJq6LRFRadnZwIkTIoQ6cgSIiQEyMsS1Zs2UUMrCAli2DPDyEkGUt7fx+kxERERERGTiaiyU+uijj/DGG2/g1q1b+Oabb+Dm5gYAOH36NMaMGVNTtyUiEtPqHB2V865dgXPndNs4Oop1nx57DCguBsz+XmJv+nTD9ZOIiIiIiKgeU0lSyUVTqLLUajWcnJyQnp4OR+0fhImo5kkScOMGcPiwMhIqIQF48ACwtBRtXngB2L0b6N5dhFCPPQa0bg2Ymxu370RERERERCaoojlJjYZSaWlp2LhxIy5evAiVSoWWLVtiypQpcHJyqqlbGgVDKSIj2LUL+O9/RQiVlFT6+u+/A23biuPcXLH+k0pl2D4SERERERHVQxXNScxqqgOnTp1C48aNsXLlSty/fx8pKSlYuXIlGjdujDNnztTUbYnI1GRlAb/8AixerBs+/fkn8PXXos7KSqwBNWcO8MMPQGqqEkgBgI0NAykiIiIiIqJapsbWlHrllVcwZMgQfPrpp7CwELcpLCzE888/j5kzZ+LQoUM1dWsiqsuSk5VpeEeOAGfOiN3yAKBFC2DUKHE8aJAImh57DOjUSQRPREREREREVGfUWCh16tQpnUAKACwsLDB79myEhYXV1G2JqC6RJKCwUFn76fvvgWHDSrfz9xfhk4+PUte2re5oKCIiIiIiolqmqAhITwfS0sSyt2lpusfaddrXDh0C3N2N129DqbFQytHREfHx8WjRooVO/a1bt9CgQYOaui0R1WZFRWLanbwo+eHDwL//DcyeLa63by8eW7cWIZS8MHlAgPH6TERERERE9Vpenm6IpF3KqpPr1eqq3fPBA4ZSj2T06NGYMmUKli9fjvDwcKhUKhw5cgSzZs3CmDFjauq2RFTbZGQAa9eKAOrYMfFrAm1HjyrHAQHA/fuAi4th+0hERERERCZNDpbkcv9+6TCprJKT8+j3t7MDnJ3FjzouLuJYu2jXubgAvr6Pfs+6oMZCqeXLl8PMzAzjx49HYWEhAMDS0hL//Oc/8Z///KembktExpSeLoKn/Hxg6FBRZ20tFinPzRXnDg5AeLgyEqpzZ93XYCBFRERERER6yFPh5FBJDpZKHusLnrKzH+3eKhXg5KQbKsnH2uclgyf50crqkd++Sar2UCo7OxuzZs3Cd999h4KCAgwbNgwvvfQSnJyc0KRJE9jZ2VX3LYnIWO7cUabhHT4M/PGHWCeqVSsllLKyEtPzXF1FEBUaCljUWB5ORERERES1XF6eEiTpC5f01cvT4iSp6vdVqZSgyNVVN1Qqq8jtnZwAM7Nq+gMgjWr/yXDBggXYvHkznn32Wdja2uLLL79EcXExduzYUd23KtO6devw/vvvIzExEa1atcKqVavQvXt3vW2//fZbrF+/HmfPnkVeXh5atWqFhQsXol+/fgbrL1Gd1Ls3sH9/6frGjYEuXcSvMczNRd2iRYbtGxERERER1bicHCA1VQmQtI/LK486asnBQTdYcnXVPdYOlbTPGSzVPtUeSn377bfYuHEjnnnmGQDAs88+i4iICBQVFcFc/gG1Bm3fvh0zZ87EunXrEBERgQ0bNqB///64cOECAvQslnzo0CH06dMH7777LpydnREVFYXBgwfjxIkTaC8vukxUHxUVAefO6Y6COn9eCZr8/MSvGkJDxTQ8eVFy7R3yiIiIiIio1svLUwKlko/l1ckrdFSFmZluoFQyWNJ3LodLnApnOlSS9CiD30qzsrJCXFwcGjZsqKmztbXFlStX4O/vX5230qtLly7o0KED1q9fr6lr2bIlhg0bhqVLl1boNVq1aoXRo0fjrbfeqlB7tVoNJycnpKenw9HRsUr9JqoVzp0DfvpJhFBHj5ZelDw2FmjXThzfvi1+ReHkZPBuEhERERFRacXFynS31FT9Rd+1Rxm5ZGGhhEZubiI0cnMrHTaVLI6OHLVkyiqak1T7SKmioiJYlYgtLSwsNIud16T8/HycPn0ac+fO1anv27cvjh07VqHXKC4uRkZGBlxdXctsk5eXh7y8PM25uqp7PBIZU0YGEBMjFhp3dhZ133yjO9XOwQGIiFBGQrVsqVzTCp6JiIiIiKh65eYqoVFKSukgKSWldMD04EHV11wyM1OCJe2Q6WF1DRqICRREVVHtoZQkSZg4cSKsra01dbm5uZg2bRrs7e01dd9++2113xopKSkoKiqCl5eXTr2XlxeSkpIq9BorVqxAVlYWRo0aVWabpUuXYhHXyKG65t49ZVHyQ4eAs2fFFL1vvwWGDxdt+vQRo6XkEIqLkhMRERERPRJJEr8PLhkoPez8UUYvNWigGx7pKyWvceQSGUO1/7Q5YcKEUnXPPfdcdd+mXKoSMa0kSaXq9Nm2bRsWLlyI77//Hp6enmW2mzdvHiIjIzXnarXaIFMTiaokJgaYMgW4eLH0taAgsTqhLCJCFCIiIiIiKkUOmFJSlCBJ+7Gs44KCqt3P3Fx/oOTuXna45OrKNZeo7qj2UCoqKqq6X7LC3N3dYW5uXmpUVHJycqnRUyVt374dU6ZMwY4dO9C7d+9y21pbW+uMBCMyOkkCrlwRI6AOHRI748kBsZeXEki1aiVGQD3+uHj08zNen4mIiIiIjEiSgMxMMaGgvGCpZPhU1YDJxqZ0oPSwc45eIlNnUvNyrKys0LFjR0RHR2O4PB0JQHR0NIYOHVrm87Zt24bJkydj27ZtGDhwoCG6SvRoiouB339XpuIdPgwkJyvXs7KUUCo4WCxe3qWL+JeNiIiIiMgE5ebqBknaRQ6eSpb8/Krdy9ZWhEdygFTesfxoZ1e975fIFJhUKAUAkZGRGDduHMLCwtCtWzd88skniI+Px7Rp0wCIqXe3b9/Gli1bAIhAavz48Vi9ejW6du2qGWVla2sLJ+4qRrVFfj6QmAgEBorzvDwRMmn/msbaGujaVYyA6tNHqVepgAEDDNtfIiIiIqJHUFQkFvHWFyiVFTBlZlbtXjY2IjTy8Kh4yMSAiah6mFwoNXr0aKSmpmLx4sVITExE69atsXv3bgT+/cN8YmIi4uPjNe03bNiAwsJC/Otf/8K//vUvTf2ECROwefNmQ3efSMjKAo4fV6bjHT8udr47c0Zct7UVU/QkSZmK16mTCKaIiIiIiGqZ7GzdQOnePd3jko/371dtFzkLCyVE0i5y4KSvMGAiMh6VJFV1w0iSqdVqODk5IT09HY6OjsbuDtVly5aJ3fBOnwYKC3WveXsDcXHiVzlEREREREZSXAw8eFB+qFSyrqo7ybm6PjxY0q53dBQTBYjIuCqak5jcSCmiOuHuXbEO1PHjIoiSVy/8/XfgxAlx7O8P9OihLEzevDn/hSUiIiKialdYKBbwlsOkh5XUVDG9rrKsrJQAycND91jfo5ubGPlERKaL/4kTGcJffylT8Q4dEjvlySZOBFq3Fscvvgg89ZQIoeT1o4iIiIiIKiEvr/RopfLKgwdVmyrn5FR2uKSvzsGBv2MlIl0MpYiqmySJMc3m5uJ86VLg9dd126hUQNu2InzSno73+OOG6ycRERER1Qn5+SI8Sk5WgiT5WF+dWl35e6hUYqqcHCg9rLi7i5FPRESPgqEU0aMqKgLOndMdCRUVBQwcKK536CDGHYeFKVPxIiIAFxfj9puIiIiIjEIOmSoSMCUnVy1kMjfXHbX0sOLqyqlyRGR4/N8OUVUkJQH//a8IoI4cAdLSdK8fOqSEUj17iuv29obuJREREREZQGGhMk0uOVk3UCp5fu8ekJ5e+XuYm+uGSJ6e5R87OyvLlhIR1VYMpYgeJicH+O03sVdsp06iLi0NmD1badOggRj91L27WJw8LEy5ZmXFsc1EREREdYi8u1x54ZL2cWpq5e/BkImIiKEUUWkZGUBMjBjtdPCgCKTy84FRo4Dt20Wb5s2BceOA9u3FdLzQUI53JiIiIqqlJEl8xXtYuCSXlJTK7y5nZiZ2i/P0VIKkkscMmYiIdPGnaCJZUZEY6fTbb6W/hXh7i28PMpUK2LLFsP0jIiIiIg3txb/LK3fvise8vMrfw8VFN1wqK2zy9BRrMsn73BARUcUwlKL65+5dZUHy9HQlXDI3FwsCFBUBQUFiBFSPHuKxcWPuX0tERERUg4qLxQoJJcOkskrJJT0rwsGhdJhU1jl3lyMiqnkMpcj0JSSIaXgHD4og6vJl5ZqFBbBunfiGAgAffyy+gQQEGKevRERERCYkN1d/yKQvcLp3T/x+sDLMzXXDpLKKl5cImuzsauZ9EhFR1TCUItMiScCNG0CjRsrIpshIYMcOpY1KBbRpo4yE0h5n3aGDYftLREREVIdIklgAvGSoVFbgpFZX/h7OzkqQ9LCwiesyERHVbQylqG6TJODiRWUU1KFDwJ07YjRUs2aiTa9ewM2bSggVESEm/RMRERER8vIqFjDdvVu10UxWVrojlkqOXtKu8/DglDkiovqEoRTVTYcPAytXiseUFN1rVlYiqJJDqWnTRCEiIiKqB+Sd5uRASftRX116euXvoW80U1nHTk5cmpOIiPRjKEW1W0EBcOaMGAnVu7cyvS4tDdi5Uxzb2gLh4WIk1OOPA126iDoiIiIiE1FUBKSm6g+VSgZOycliLafKsLQsvQZTeaObOJqJiIiqA0Mpql1yc4HffhPT8A4eBGJigKwsce2NN5RQ6rHHgKVLxXS8jh35zYiIiIjqnLy8h49iko9TUsTudJXh4KAESvoetY+dnTmaiYiIDI+hFBmXJCnfgG7cAEJCxDc0ba6uYgRUaKhS5+ICzJ1ruH4SERERPYQkAZmZuoFSyYDpUabNqVSAm1v5QZP2I3eaIyKi2o6hFBlWejpw9KgYBXXwoAihNm0S14KCxLcnFxdlKt7jjwOtWnFbFSIiIjIK7d3myguY5JKTU7nXl6fNySOXygua3N0BC357JyIiE8J/1qjm7doFHDggpuSdPas79vzOHWW0lJkZcP484O3N8eNERERUY4qKxHQ47TBJX8Ak11V2tzk7O/0hk75zTpsjIqL6jKEUVa+kJODPP8Wi5LIFC0QYJWvcWKwFJRftb2I+PgbrKhEREZmO/Hzg3r3SoZK+kKkq6zM5Oz88YJKLvX2NvEUiIiKTw1CKHk18vLIo+aFDwJUrYtHxtDRlB7yxY4Fu3cRUvO7dgYYNjdplIiIiqhtych4+kkkuDx5U7rVVKjEdrrxwSXvXOWvrmnmPRERE9ZlJhlLr1q3D+++/j8TERLRq1QqrVq1C9+7dy2x/8OBBREZG4vz58/D19cXs2bMxbdo0A/a4DvrwQ+CDD4CbN3XrVSqxTtSdO2JEFADMmmXw7hEREVHtIy8EXtYIppJ1GRmVe31z8/LDJe1zrs9ERERkfCb3T/H27dsxc+ZMrFu3DhEREdiwYQP69++PCxcuICAgoFT7uLg4DBgwAFOnTsUXX3yBo0ePYvr06fDw8MCIESOM8A5qEUkCLl5URkL95z9AYKC4VlAgAilzc6BjRzEKqkcPICJCLFRORERE9YIkiX1MHjZtrqoLgVtblz+SSTt0cnXl3ihERER1iUqSJMnYnahOXbp0QYcOHbB+/XpNXcuWLTFs2DAsXbq0VPs5c+Zg165duHjxoqZu2rRp+P333xETE1Ohe6rVajg5OSE9PR2Ojo6P/iaMpagIOHdOCaEOHxaLM8g2bwYmTBDH8fHApUtiWl6DBkbpLhEREdWM4mLg/v2KjWa6e1es51QZJRcCL684OnIhcCIiorqmojmJSY2Uys/Px+nTpzF37lyd+r59++LYsWN6nxMTE4O+ffvq1PXr1w8bN25EQUEBLC0tSz0nLy8PeXl5mnO1Wl0Nva8Fdu0C/vEP3TpbWxE89egBdOqk1AcEiEJERER1Qlk7zukr9+5Vfsc5R8eKB01cCJyIiIgAEwulUlJSUFRUBC8vL516Ly8vJCUl6X1OUlKS3vaFhYVISUmBj57d4JYuXYpFixZVX8dri8ceE98o5RCqRw8gLEwsXE5ERES1TkFBxXacu3u3ajvOubhULGTy9FT2NyEiIiKqKJMKpWSqEmO8JUkqVfew9vrqZfPmzUNkZKTmXK1Ww9/fv6rdrT08PMRYfXNzY/eEiIio3srLKz9c0p5Cl5paudcuueNceQuCe3ry91JERERUs0wqlHJ3d4e5uXmpUVHJycmlRkPJvL299ba3sLCAm5ub3udYW1vD2lT3BWYgRUREVO2ysspej6lkSU+v3Gubm4vfK1VkRBN3nCMiIqLaxKS+llhZWaFjx46Ijo7G8OHDNfXR0dEYOnSo3ud069YNP/zwg07dzz//jLCwML3rSRERERFJEpCRUfEd57KyKvf6lpYP321OLm5u3HGOiIiI6iaTCqUAIDIyEuPGjUNYWBi6deuGTz75BPHx8Zg2bRoAMfXu9u3b2LJlCwCx097atWsRGRmJqVOnIiYmBhs3bsS2bduM+TaIiIjIwCQJePDg4QGTPOIpN7dyr29jU7G1mby8xFpO3HGOiIiITJ3JhVKjR49GamoqFi9ejMTERLRu3Rq7d+9GYGAgACAxMRHx8fGa9sHBwdi9ezdeeeUVfPTRR/D19cWaNWswYsQIY70FIiIiqiYld5wrawpdcrIoBQWVe30Hh4cHTHJp0IBBExEREZE2lSSv6k1Vplar4eTkhPT0dDg6Ohq7O0RERCYtP18JkR62EHhVdpxzdn54wCQXO7saeYtEREREdVpFcxKTGylFREREdU92tv6QSV/dgweVe215x7mygiXtek9PwFT3MiEiIiKqbRhKERERUbWTJLGLnL5wSd9xZmblXt/cXH/IpK+OO84RERER1U78ikZEREQVor0+08NCpuRkMc2uMqytKzZlTl4InDvOEREREdVtDKWIiIjqsdxc3SCpvMApJUWMgKoMR0f9U+T0HXMhcCIiIqL6haEUERGRCZEkIC2t7KBJ+zE5GVCrK/f6+tZnKu/YxqZG3iYRERERmQCGUkRERLVcQQFw717Fg6aCgsq9vpWVEiZ5epYfMnF9JiIiIiKqLvxaSUREZGCSBGRk6AZJcilZd/cucP9+5e/h5KQbNJV81D52cuK0OSIiIiIyPIZSRERE1UAezVSRoCk5GcjLq9zrm5sDHh4VC5o8PDhtjoiIiIhqP4ZSREREekgSkJ5efrCkXffgQeXv4eBQOlTSPvfwUKbOubpytzkiIiIiMi0MpYiIqN7IzhYBkrw+U1lFvl7ZtZm0RzOVDJj0BU52djXzPomIiIiI6gKGUkREVGcVFAApKfoDJX0lK6vy93Bw0D9NTt85RzMREREREVUcQykiIqo1iorEot5ysFTWo1yqsgC4vNNceUUe7eThAdjaVv/7JCIiIiIihlJERFSDiouBtLTyAybtoCk1VTynMszMAHf30oFSWaVBA+40R0RERERUGzCUIiKiCpMX/35YwKT9WFRU+fu4uOiGSx4eZYdNrq5iLSciIiIiIqpbGEoREdVjJUcy6Sva11JSKr/4NwA4OuqfGqfv0d0dsLSs9rdKRERERES1DEMpIiITUlws1lkqK2QqWZ+SUrWRTA4OpUcylfXo4QFYW1f/eyUiIiIiorqNoRQRUS2Wny+Co5JBUlnnVVmTCRAjmbSnyMnHJYs8komLfxMRERER0aNiKEVEZCCSBGRmPjxY0j5Xq6t2L2fnh4dMcr27O0cyERERERGR4TGUIiKqooICMVVODpHkon1eMmTKy6v8feTd5eQASTtY0j6Xd6DjmkxERERERFQXMJQiIoKyq5y+YElf0JSSIhYIrwobm7KDJX3nzs4imCIiIiIiIjIlJhVKPXjwADNmzMCuXbsAAEOGDMGHH34IZ2dnve0LCgrwxhtvYPfu3bhx4wacnJzQu3dv/Oc//4Gvr68Be05E1UmSgOxs3VBJu6Sm6g+eCgsrfy+VCnB11R3JJBcPD8DNrfS0OTs78TwiIiIiIqL6zKRCqbFjxyIhIQF79uwBALzwwgsYN24cfvjhB73ts7OzcebMGbz55psIDQ3FgwcPMHPmTAwZMgSnTp0yZNeJqBw5OWUHS2WFTrm5VbuXvb1uuKQvaNI+d3UFzM2r9/0SERERERHVBypJkiRjd6I6XLx4ESEhITh+/Di6dOkCADh+/Di6deuGS5cuoXnz5hV6nZMnT6Jz587466+/EBAQUKHnqNVqODk5IT09HY6OjlV+D0SmTpKArCwlUEpN1T0uqy47u2r3s7bWDZDc3HSPtafKyXXcVY6IiIiIiOjRVDQnMZmRUjExMXByctIEUgDQtWtXODk54dixYxUOpdLT06FSqcqc8gcAeXl5yNNarVhd1e2xiOow7TWYSgZJ5QVN+flVu5+lpW7ApC9oKllvb89pckRERERERLWVyYRSSUlJ8PT0LFXv6emJpKSkCr1Gbm4u5s6di7Fjx5ab5C1duhSLFi2qcl+Japu8PCU4qmh58AAoKqra/eQRTHKg5Oame6wvbHJwYMBERERERERkSmp9KLVw4cKHBkAnT54EAKj0/MQqSZLe+pIKCgrwzDPPoLi4GOvWrSu37bx58xAZGak5V6vV8Pf3f+g9iGpaUZEIi+7fF8FRyceySlWnxwFiNFJ5wZK+Oi70TURERERERLU+lHrppZfwzDPPlNsmKCgIf/zxB+7evVvq2r179+Dl5VXu8wsKCjBq1CjExcXhl19+eei6UNbW1rC2tn5454mqqLhYTI3TFyzpe5SP09Kqfk9zc7Fot6urEiY9rLi6AjY21fa2iYiIiIiIqB6p9aGUu7s73N3dH9quW7duSE9Px2+//YbOnTsDAE6cOIH09HSEh4eX+Tw5kLp69SoOHDgANze3aus7UWGhMnKpMuXBA7FmU1U5OirhUkWDJkdHwMys+t47ERERERERUXlMZvc9AOjfvz/u3LmDDRs2AABeeOEFBAYG4ocfftC0adGiBZYuXYrhw4ejsLAQI0aMwJkzZ/Djjz/qjKhydXWFlZVVhe7L3fdMm7xjnBwuaYdM5dXdvw886hr4Dg664VLJkEnfo4uLWBSciIiIiIiIyBjq3e57ALB161bMmDEDffv2BQAMGTIEa9eu1Wlz+fJlpKenAwASEhKwa9cuAEC7du102h04cABPPPFEjfeZDCc3VwRG+oocJpUMmeTHgoJHu7ezsxImaRcXF/318jXOEiUiIiIiIiJTZVIjpYyFI6UMJydHCY/S0soOmfSVnJxHu7elZekgqeSxi4vuaCZXVxFImZtXx7snIiIiIiIiqv3q5Ugpqv2Ki8WUNjlQethjyeO8vEe7v0qlhEdlFTc3JWzSDp24YxwRERERERFR9WEoRZVSXAxkZoqgqGRJT1dCJLmUPE9Pf7QFvAGxGLezs/5ASbtee/SSXLiYNxEREREREVHtwFCKAAAJCcDXX5cOkEqep6eLYOpR2doqAVJ5j/rCpwYNOGKJiIiIiIiIqK5jKEUAgJs3gVdeqXh7S0vd4EguTk66o5a0gyXtcy7gTURERERERFS/MZQiAICfH/DMM0qopB0wOTkp5/KjrS1HKxERERERERFR1TGUIgBAUBCwbZuxe0FERERERERE9QWXfCYiIiIiIiIiIoNjKEVERERERERERAbHUIqIiIiIiIiIiAyOoRQRERERERERERkcQykiIiIiIiIiIjI4hlJERERERERERGRwFsbugCmQJAkAoFarjdwTIiIiIiIiIiLjkvMROS8pC0OpapCRkQEA8Pf3N3JPiIiIiIiIiIhqh4yMDDg5OZV5XSU9LLaihyouLsadO3fQoEEDqFQqY3enytRqNfz9/XHr1i04OjoauztkQPzs6y9+9vUXP/v6i599/cXPvv7iZ1+/8fOvv4z52UuShIyMDPj6+sLMrOyVozhSqhqYmZnBz8/P2N2oNo6OjvyfVT3Fz77+4mdff/Gzr7/42ddf/OzrL3729Rs///rLWJ99eSOkZFzonIiIiIiIiIiIDI6hFBERERERERERGRxDKdKwtrbGggULYG1tbeyukIHxs6+/+NnXX/zs6y9+9vUXP/v6i599/cbPv/6qC589FzonIiIiIiIiIiKD40gpIiIiIiIiIiIyOIZSRERERERERERkcAyliIiIiIiIiIjI4BhKERERERERERGRwTGUqmfWrVuH4OBg2NjYoGPHjjh8+HC57Q8ePIiOHTvCxsYGjRo1wscff2ygnlJ1q8xn/+2336JPnz7w8PCAo6MjunXrhr179xqwt1SdKvvfvezo0aOwsLBAu3btaraDVGMq+9nn5eVh/vz5CAwMhLW1NRo3boxNmzYZqLdUnSr72W/duhWhoaGws7ODj48PJk2ahNTUVAP1lqrLoUOHMHjwYPj6+kKlUuG777576HP4Xc80VPaz53c901GV/+5l/K5Xt1Xls6+N3/UYStUj27dvx8yZMzF//nzExsaie/fu6N+/P+Lj4/W2j4uLw4ABA9C9e3fExsbi9ddfx4wZM/DNN98YuOf0qCr72R86dAh9+vTB7t27cfr0afTs2RODBw9GbGysgXtOj6qyn70sPT0d48ePx5NPPmmgnlJ1q8pnP2rUKOzfvx8bN27E5cuXsW3bNrRo0cKAvabqUNnP/siRIxg/fjymTJmC8+fPY8eOHTh58iSef/55A/ecHlVWVhZCQ0Oxdu3aCrXndz3TUdnPnt/1TEdlP3sZv+vVfVX57Gvldz2J6o3OnTtL06ZN06lr0aKFNHfuXL3tZ8+eLbVo0UKn7sUXX5S6du1aY32kmlHZz16fkJAQadGiRdXdNaphVf3sR48eLb3xxhvSggULpNDQ0BrsIdWUyn72//vf/yQnJycpNTXVEN2jGlTZz/7999+XGjVqpFO3Zs0ayc/Pr8b6SDUPgLRz585y2/C7nmmqyGevD7/r1X2V+ez5Xc+0VOSzr63f9ThSqp7Iz8/H6dOn0bdvX536vn374tixY3qfExMTU6p9v379cOrUKRQUFNRYX6l6VeWzL6m4uBgZGRlwdXWtiS5SDanqZx8VFYXr169jwYIFNd1FqiFV+ex37dqFsLAwLFu2DA0bNkSzZs3w2muvIScnxxBdpmpSlc8+PDwcCQkJ2L17NyRJwt27d/H1119j4MCBhugyGRG/65GM3/XqF37Xq59q63c9C6PenQwmJSUFRUVF8PLy0qn38vJCUlKS3uckJSXpbV9YWIiUlBT4+PjUWH+p+lTlsy9pxYoVyMrKwqhRo2qii1RDqvLZX716FXPnzsXhw4dhYcF/Iuqqqnz2N27cwJEjR2BjY4OdO3ciJSUF06dPx/37942+1gBVXFU++/DwcGzduhWjR49Gbm4uCgsLMWTIEHz44YeG6DIZEb/rkYzf9eoPfterv2rrdz2OlKpnVCqVzrkkSaXqHtZeXz3VfpX97GXbtm3DwoULsX37dnh6etZU96gGVfSzLyoqwtixY7Fo0SI0a9bMUN2jGlSZ/+6Li4uhUqmwdetWdO7cGQMGDMAHH3yAzZs3G/03aFR5lfnsL1y4gBkzZuCtt97C6dOnsWfPHsTFxWHatGmG6CoZGb/rEb/r1R/8rle/1dbveoxG6wl3d3eYm5uX+i1pcnJyqd+Qyby9vfW2t7CwgJubW431lapXVT572fbt2zFlyhTs2LEDvXv3rsluUg2o7GefkZGBU6dOITY2Fi+99BIA8Y+XJEmwsLDAzz//jF69ehmk7/RoqvLfvY+PDxo2bAgnJydNXcuWLSFJEhISEtC0adMa7TNVj6p89kuXLkVERARmzZoFAGjbti3s7e3RvXt3LFmyhKNlTBi/6xG/69Uv/K5Xv9XW73ocKVVPWFlZoWPHjoiOjtapj46ORnh4uN7ndOvWrVT7n3/+GWFhYbC0tKyxvlL1qspnD4jfmk2cOBFffvkl1xWpoyr72Ts6OuLcuXM4e/aspkybNg3NmzfH2bNn0aVLF0N1nR5RVf67j4iIwJ07d5CZmampu3LlCszMzODn51ej/aXqU5XPPjs7G2Zmul8Jzc3NASijZsg08bte/cbvevUPv+vVb7X2u55Rllcno/jqq68kS0tLaePGjdKFCxekmTNnSvb29tLNmzclSZKkuXPnSuPGjdO0v3HjhmRnZye98sor0oULF6SNGzdKlpaW0tdff22st0BVVNnP/ssvv5QsLCykjz76SEpMTNSUtLQ0Y70FqqLKfvYlcUeWuquyn31GRobk5+cnjRw5Ujp//rx08OBBqWnTptLzzz9vrLdAVVTZzz4qKkqysLCQ1q1bJ12/fl06cuSIFBYWJnXu3NlYb4GqKCMjQ4qNjZViY2MlANIHH3wgxcbGSn/99ZckSfyuZ8oq+9nzu57pqOxnXxK/69Vdlf3sa+t3PYZS9cxHH30kBQYGSlZWVlKHDh2kgwcPaq5NmDBB6tGjh077X3/9VWrfvr1kZWUlBQUFSevXrzdwj6m6VOaz79GjhwSgVJkwYYLhO06PrLL/3WvjF5W6rbKf/cWLF6XevXtLtra2kp+fnxQZGSllZ2cbuNdUHSr72a9Zs0YKCQmRbG1tJR8fH+nZZ5+VEhISDNxrelQHDhwo999vftczXZX97Pldz3RU5b97bfyuV3dV5bOvjd/1VJLEcdlERERERERERGRYXFOKiIiIiIiIiIgMjqEUEREREREREREZHEMpIiIiIiIiIiIyOIZSRERERERERERkcAyliIiIiIiIiIjI4BhKERERERERERGRwTGUIiIiIiIiIiIig2MoRUREREREREREBsdQioiIiIiIiIiIDI6hFBERERERERERGRxDKSIiIiIiIiIiMjiGUkREREREREREZHAMpYiIiIiIiIiIyOAYShERERERERERkcExlCIiIiIiIiIiIoNjKEVERERERERERAZnYewOmILi4mLcuXMHDRo0gEqlMnZ3iIiIiIiIiIiMRpIkZGRkwNfXF2ZmZY+HYihVDe7cuQN/f39jd4OIiIiIiIiIqNa4desW/Pz8yrzOUKoaNGjQAID4w3Z0dDRyb4iIiIiIiIiIjEetVsPf31+Tl5SFoVQ1kKfsOTo6MpQiIiIiIiIiIgIeusQRFzonIiIiIiIiIiKDYyhFREREREREREQGZ3Kh1KFDhzB48GD4+vpCpVLhu+++e+hzDh48iI4dO8LGxgaNGjXCxx9/XPMdJSIiIiIiIiKqx0xuTamsrCyEhoZi0qRJGDFixEPbx8XFYcCAAZg6dSq++OILHD16FNOnT4eHh0eFnk9ERERERERUWcXFxcjPzzd2N4iqxNLSEubm5o/8OiYXSvXv3x/9+/evcPuPP/4YAQEBWLVqFQCgZcuWOHXqFJYvX85QioiIiIiIiKpdfn4+4uLiUFxcbOyuEFWZs7MzvL29H7qYeXlMLpSqrJiYGPTt21enrl+/fti4cSMKCgpgaWlppJ4ZQVERkJWlWyf/5VKpACsrUQBAkoCCAsDMTFyTH4mIiIiIiKhMkiQhMTER5ubm8Pf3h5mZya2qQyZOkiRkZ2cjOTkZAODj41Pl16r3oVRSUhK8vLx06ry8vFBYWIiUlBS9f7h5eXnIy8vTnKvV6hrvp0H8+SfQrl3Z1+fNA959VxxfuwY0a1a6jUoFmJsDL78MfPCBqLt7F2jZUgRX5uaiWFgoZdQoYMkS0TYrC+jTR7eNpaUIwywtge7dgRkzRNviYiAyUtRrt7GyAqytgSZNgAEDlL7t3Ste19q6dGnQAHB3f+Q/QiIiIiIiovIUFhYiOzsbvr6+sLOzM3Z3iKrE1tYWAJCcnAxPT88qT+Wr96EUgFJDzSRJ0lsvW7p0KRYtWlTj/arV/v4z0ltfWCgCI1lBAfDgQdmvde+ecpyfD8TElN1WHqklv+7q1WW3HTpUN5QaNEj0TZ8nnwT27VPOfX2BnBzA1rZ0ad9e975vvqm0tbMTxd5eFG9voGdPpe3t2yI4s7cX7Ti6jIiIiIioXikqKgIAWGn/bENUB8mhakFBAUOpqvL29kZSUpJOXXJyMiwsLODm5qb3OfPmzUNkZKTmXK1Ww9/fv0b7aRBt2gC5ucq5HDxJkigWWn9dGjcWQZMkiQCqZNFO/L28gIsXxfTA4mIRDBUViVJYCHh6Km3t7YHvvhP1cikoEGFVQQHQtKnSVqUSo7cKCnTb5OcDeXlAWJjuewkNFfX6yt8pr8aDB+LPIi2t9J9TyeG1GzboBmvaOnQATp9Wzh9/HLhxQzm3swMcHMT7DgkBfvxRuTZ/PnD/PuDoKEZyOToqx+7uQI8eStvsbDHiqxoWmiMiIiIiopr3KOvwENUG1fF3uN6HUt26dcMPP/ygU/fzzz8jLCyszPWkrK2tYW1tbYjuGZaZmQg2KsLcHHB2rlhbS0ugRYuKtbWyEiOcKtpWnk74MCoVcOpUxdoCwOXLYvRTTo4IfOTjnBzAxUW37cyZIsSS22Zni2mIWVm6IRqgO4IMUNoDInDS9n//J6ZJ6hMcrBtuPf64CL/s7ZUAS3708wO2bFHa7tgBpKeLz8/FRTzKxclJN3wkIiIiIiIiqiEm99NnZmYmrmn9IB8XF4ezZ8/C1dUVAQEBmDdvHm7fvo0tf/+QPm3aNKxduxaRkZGYOnUqYmJisHHjRmzbts1Yb4Fqg4CAird9/fWKt42LE8GUdnCVlQVkZpYOg157DUhMBDIyALVa97HkWmfyumby62mP/gsO1m27bFnZAZ2LixidJYuMBK5e1Q2u5DDL1RUYNkxpW1Ag3gN/40NERERERLXME088gXbt2mHVqlWP9DoTJ05EWloavvvuu2rpV31ncqHUqVOn0FNrDR95mt2ECROwefNmJCYmIj4+XnM9ODgYu3fvxiuvvIKPPvoIvr6+WLNmDUaMGGHwvlM9YWYmpuw5OJTf7sUXK/6a587pD6/U6tJhV8+eItR68EBMT5RLZmbp0W+HD5cdYDk764ZSAwcChw4Bbm6li7u7WMxeDqwuXxbhnJubCLjq0y6XRERERER1zMOmack/b+trFxERgSNHjmjODxw4gPfffx8nTpxATk4OgoKC0L9/f0RGRqJhw4Z6Xz82NhZvvvkmfvvtN6jVanh7e6NLly746KOP4F5DG1bdvHkTwcHBiI2NRTutDcFWr16tWYeaHp3JhVJPPPFEuX9BNm/eXKquR48eOHPmTA32iqiGybsIVuR/yMuW6a8vLBTBlLYlS4CEBCW40g6ySq7DlZoq1ue6c0cUbS4uwDvvKOcvvwxERyvnjo66Adbu3UqAtX+/mG7o6akUJyeOyCIiIiIiMpDExETN8fbt2/HWW2/h8uXLmjpbrZ8NoqKi8NRTT2nOtRd037BhA6ZPn44JEybgm2++QVBQEOLj47FlyxasWLECH8g7uGtJTk5G7969MXjwYOzduxfOzs6Ii4vDrl27kC0vhWJATk5OBr+nKTO5UIqIqsjCovRIqX79Kv78X38VwVRqqpgCKB+nppZua2cn7iUvJK9WixIXJ+q1A6f33tMNsAAxssrDQyyif+qUsvj899+LRee1AywPDzEqjSEWEREREVGVeHt7a46dnJygUql06rQ5OzvrvZaQkIAZM2ZgxowZWLlypaY+KCgIjz/+ONL0bTIF4NixY1Cr1fjss89g8fcskODgYPTq1Uun3cGDBzFr1iz8/vvvcHV1xYQJE7BkyRLNc0pSqVTYuXMnhmnN/nB2dsaqVaswceJEBP+9DEr79u0BiMEsv/76a6npe3l5eZg1axa++uorqNVqhIWFYeXKlejUqRMA4Ndff0XPnj2xb98+zJkzBxcuXEC7du0QFRWF5s2b6+1bfcJQioiqR4MGogQFPbytPP+6qEiMvtIOs/LydNu2aiVGcCUni5KRIdavunNH7JCovRvi2rXAvn2l72djA3h7A9evK+2//FK8ho+PKN7e4rFkKEZEREREVIMkSdn7yNDs7Az31XfHjh3Iz8/H7Nmz9V53LmMjLW9vbxQWFmLnzp0YOXKk3imCt2/fxoABAzBx4kRs2bIFly5dwtSpU2FjY4OFCxdWqb+//fYbOnfujH379qFVq1Y6I760zZ49G9988w0+//xzBAYGYtmyZejXrx+uXbsGV1dXTbv58+djxYoV8PDwwLRp0zB58mQcPXq0Sn0zJQyliMh4zM3FdL3yph1q/RYFgAii7t0TpeR0w/BwMY0xOVlcv3tX7IqYmyvCLO0Aa9MmMTWwJGtrEU5duyb6BwA7dwIpKboBlpcXdyokIiIiokeWnf3w5WZrSmam2MC7Oo0ZMwbm8vdoAF988QWGDRuGq1evwtHRET4lN216iK5du+L111/H2LFjMW3aNHTu3Bm9evXC+PHj4eXlBQBYt24d/P39sXbtWqhUKrRo0QJ37tzBnDlz8NZbb8FM++eACvLw8AAAuLm5lTkqLCsrC+vXr8fmzZvRv39/AMCnn36K6OhobNy4EbNmzdK0feedd9CjRw8AwNy5czFw4EDk5ubCxsam0n0zJfyJiojqFhsbwN9flJIWLSpdl5UlAip5h0JZ//4iWEpKErscJiaK6YR5eeI5Wv+QYu1a4JdfdJ+vUokwrWFD4PRpJfDau1esgSUHWD4+1f8vPRERERFRLbVy5Ur07t1bcy6HUJIkPXTB9LK88847iIyMxC+//ILjx4/j448/xrvvvotDhw6hTZs2uHjxIrp166bz+hEREcjMzERCQgICKrO7eiVcv34dBQUFiIiI0NRZWlqic+fOuHjxok7btm3bao7lP5Pk5OQa61tdwVCKiEybvb3+UOjVV0vX5eaKkCo9Xbe+e3exsHtiorh+966YenjvngintH/z8t57wIEDus93cgL8/ICAAODHH5X2v/8uHv38AFdXThskIiIiqofs7EpPADDkvaubt7c3mjRpUqq+WbNmSE9PR2JiYqVHSwFixNLTTz+Np59+GkuXLkX79u2xfPlyfP7553oDL3kDtLKCMJVKVWqTtIKCgkr1qax76OuPpdaO4/K14uLiSt3PFDGUIiKS2djoXxOr5Dz0oiKxBlZiYulvEO3bi50M5dFXWVki5EpPF1MAtQOsV15RAiwbGxFO+fmJ0VcBAWLHQvkfM7VahGvaI7iIiIiIqM5TqerHwPqRI0di7ty5WLZsmc5C57K0tLQy15UqycrKCo0bN0ZWVhYAICQkBN98841OGHTs2DE0aNAADRs21PsaHh4eOrsKXr16VWc3P3kNqaKiojL70aRJE1hZWeHIkSMYO3YsABFsnTp1CjNnzqzQe6nvGEoREVWWubmyu19JK1bonmdkALdvAwkJpVewdHQUUwBTUsQorWvXRAHEulXvvqu0HToUOHIE8PUVoVXJAOvpp6v3PRIRERERVSN/f3+sXLkSL730EtRqNcaPH4+goCAkJCRgy5YtcHBwwIqS36UB/Pjjj/jqq6/wzDPPoFmzZpAkCT/88AN2796NqKgoAMD06dOxatUqvPzyy3jppZdw+fJlLFiwAJGRkWWuJ9WrVy+sXbsWXbt2RXFxMebMmaMzmsnT0xO2trbYs2cP/Pz8YGNjAycnJ53XsLe3xz//+U/MmjULrq6uCAgIwLJly5CdnY0pU6ZU45+e6WIoRURUkxo0AFq0EKUkeRfC3FyxE2BCghJglZSYKEZgxceLos3bWzeUevZZ0SYwsHQJCKiZcdpERERERA8xffp0NGvWDMuXL8fw4cORk5ODoKAgDBo0CJGRkXqfExISAjs7O7z66qu4desWrK2t0bRpU3z22WcYN24cAKBhw4bYvXs3Zs2ahdDQULi6umLKlCl44403yuzLihUrMGnSJDz++OPw9fXF6tWrcfr0ac11CwsLrFmzBosXL8Zbb72F7t2749dffy31Ov/5z39QXFyMcePGISMjA2FhYdi7dy9cXFwe7Q+rnlBJJSdRUqWp1Wo4OTkhPT0djo6Oxu4OEZmiwkKxllVCgm54lZAggq8NG5S2TZoA16/rfx15cXfZ+vVAfr5uaMX1rYiIiIhqTG5uLuLi4hAcHFzvd16juq28v8sVzUk4UoqIqC6wsBBT9Ro2BLp0Kb/tl18CcXHAX3+VLoGBum1XrCgdYDk4iHCqQwfgv/9V6s+fF4u2+/hwbSsiIiIiInpkDKWIiExN586i6JOTo3s+ahRw9aoSWiUni8XbL1wQ4ZS2oUNFgGVpKdazCgoCGjUCGjcGWrUChgypkbdDRERERESmiaEUEVF9Ymure669mDogQqv4eBFQaS8KKUlidJS5OVBQIEZixcUpuwd26qQbSg0bJto2aqSUxo3FCKy/dzIhIiIiIqL6jaEUEREpbG2B5s1F0aZSAZcvi7WtEhNFaHXzJnDjhijBwUrboiLgf/8Ta1WVZGYGDBgA/PCDUvfjj2Inw0aNADc3rmdFRERERFRPMJQiIqKKs7AA/P1Feewx/W0kCfj2WyWw0i7Z2bq7/xUXAyNGKAFWgwa6I6u6dhXXiYiIiIjI5DCUIiKi6mVhAQwcWLpeksSaVXl5Sp1aLRZuv3FD7CiYkQH8/rsoADBypBJKFReLtav8/IBmzYCmTZXHoCCx1hUREREREdUZDKWIiMgwVCrAy0u3ztkZOHRIHOfk6E4JvHEDaNdOaXvnDnDpkij79um+joUF8PzzwPr14lySgP37gSZNxKgu7hZIRERERFTrMJQiIqLawdYWaNlSFH3c3YHDh8VugVeuiEe55OSIqX+ypCSgTx9xbG0tpgJqj6zq2hVo06bm3xMREREREZWJoRQREdUNNjZiHauSa1kVF4tRVNqjoe7fB1q0AK5fF9MFL1wQRRYZCaxYIY5TUoDp05XASi7u7lx0nYiIiIioBpk9vAkREVEtZmYm1pny8VHqWrUCLl4UC6tfvw7s2QN8+CHw8svAU08BnTsrbS9fBnbsAN55B5g4EYiIELsBurqKdv/9r9K2sFB3TSwiIiIiqnZBQUFYtWrVI73Gr7/+CpVKhbS0tGrp082bN6FSqXD27Nlqeb2yTJw4EcOGDXvk11m4cCHaaS+FUUsxlCIiItNlYSF28uvXD3jpJWDNGuB//wNGj1baBAQAH3wATJsGPPmkWIMKANLSgJMnxWLssjNnAHt7MapqyBBgzhwgKgo4fly0JyIiIjJxx44dg7m5OZ566iljd0XjiSeewMyZM3XqwsPDkZiYCCcnJ4P148aNGxgzZgx8fX1hY2MDPz8/DB06FFeuXKnR+6pUKnz33Xc6da+99hr2799fo/etDpy+R0RE9Zu/P/DKK7p1OTlihNWVK7qLrV++DBQVKWtZ/fCD7vPWrxfhFgDcvQucOyfWyPL15VRAIiIiMgmbNm3Cyy+/jM8++wzx8fEICAgwdpf0srKygre3t8Hul5+fjz59+qBFixb49ttv4ePjg4SEBOzevRvp6ekG64fMwcEBDg4OBr9vZXGkFBERUUm2tkDr1sA//iFGWsmeew64fVvs/rd2LfCvf4nRVb6+4npwsNJ2/36x2LqfH+DkJKYCjh8PLF0K7NwJ3Ltn2PdERERE9IiysrLwf//3f/jnP/+JQYMGYfPmzTrX5Slz+/fvR1hYGOzs7BAeHo7Lly9r2ly/fh1Dhw6Fl5cXHBwc0KlTJ+wrubOylsmTJ2PQoEE6dYWFhfD29samTZswceJEHDx4EKtXr4ZKpYJKpcLNmzf1Tt87evQoevToATs7O7i4uKBfv3548OABAGDPnj147LHH4OzsDDc3NwwaNAjXr1+v8J/NhQsXcOPGDaxbtw5du3ZFYGAgIiIi8M4776BTp06adufOnUOvXr1ga2sLNzc3vPDCC8jMzCzzdfVNZWzXrh0WLlyouQ4Aw4cPh0ql0pyXnL5XXFyMxYsXw8/PD9bW1mjXrh327NmjuS5PT/z222/Rs2dP2NnZITQ0FDExMRX+M6gKhlJEREQVpVKJAOrJJ0UgtXatCKhu3wbS04EnnlDaSpKY5mduDmRkiKmA//0v8PrrIuw6flxpGxMDzJ8vrp86JdoTERFR/ZKVVXbJza1425ycirWtgu3bt6N58+Zo3rw5nnvuOURFRUGSpFLt5s+fjxUrVuDUqVOwsLDA5MmTNdcyMzMxYMAA7Nu3D7GxsejXrx8GDx6M+Ph4vfd8/vnnsWfPHiQmJmrqdu/ejczMTIwaNQqrV69Gt27dMHXqVCQmJiIxMRH+8nIMWs6ePYsnn3wSrVq1QkxMDI4cOYLBgwejqKjo7z+mLERGRuLkyZPYv38/zMzMMHz4cBQXF1foz8bDwwNmZmb4+uuvNa9ZUnZ2Np566im4uLjg5MmT2LFjB/bt24eXXnqpQvfQ5+TJkwCAqKgoJCYmas5LWr16NVasWIHly5fjjz/+QL9+/TBkyBBcvXpVp938+fPx2muv4ezZs2jWrBnGjBmDwsLCKvfvYTh9j4iIqDo4OuqeP/usKPn5wLVrYuH1S5eUx1atlLb79gHvvqv7fD8/ICREjNh66SXdUVhERERkesqbajVgAPDTT8q5p6fY0EWfHj2AX39VzoOCxG7DJekJkx5m48aNeO655wAATz31FDIzM7F//3707t1bp90777yDHj16AADmzp2LgQMHIjc3FzY2NggNDUVoaKim7ZIlS7Bz507s2rVLbzgTHh6O5s2b47///S9mz54NQAQwTz/9tGZ6mpWVFezs7Mqdrrds2TKEhYVh3bp1mrpWWt/HRowYUeq9enp64sKFC2jduvVD/2waNmyINWvWYPbs2Vi0aBHCwsLQs2dPPPvss2j098j7rVu3IicnB1u2bIG9vT0AYO3atRg8eDDee+89eHl5PfQ+JXl4eAAAnJ2dy33/y5cvx5w5c/DMM88AAN577z0cOHAAq1atwkcffaRp99prr2HgwIEAgEWLFqFVq1a4du0aWrRoUem+VQRHShEREdUkKysRLo0YIUZDffGFGA2lPS2wUyfgxRfFl0hPT1GXkAD8/LNYhF37N56bNgFDh4rX+vJL4I8/uCMgERER1bjLly/jt99+04QaFhYWGD16NDZt2lSqbdu2bTXHPn/vkJycnAxAjEiaPXs2QkJC4OzsDAcHB1y6dKnMkVKAGC0VFRWleZ2ffvpJZ/RVRcgjpcpy/fp1jB07Fo0aNYKjoyOC//6FYHn9Kulf//oXkpKS8MUXX6Bbt27YsWMHWrVqhejoaADAxYsXERoaqgmkACAiIgLFxcU6Uxyrm1qtxp07dxAREaFTHxERgYsXL+rUlffZ1QSOlCIiIjK2p54SRXb/vhhNdf68KE2bKtcOHgR27RJFZm4upgq2bg18+CFQhd+yERERkZGVs64QzM11z8sLCcxKjD25ebPKXdK2ceNGFBYWomHDhpo6SZJgaWmJBw8ewMXFRVNvaWmpOVb9vdmLPA1u1qxZ2Lt3L5YvX44mTZrA1tYWI0eORH5+fpn3Hj9+PObOnYuYmBjExMQgKCgI3bt3r1T/bW1ty70+ePBg+Pv749NPP4Wvry+Ki4vRunXrcvulT4MGDTBkyBAMGTIES5YsQb9+/bBkyRL06dMHkiRp/jxKKqvezMys1BTJgoKCSvWprHvo6095n11NYChFRERU27i6AuHhopQ0Y4ZYNP3PP5WSlqZMC/z8c6XtzJkixGrdWkwXbN1alICA0l9YiYiIyLi0Rs8YrW0ZCgsLsWXLFqxYsQJ9+/bVuTZixAhs3bq1wusiHT58GBMnTsTw4cMBiDWmbj4kOHNzc8OwYcMQFRWFmJgYTJo0See6lZVVmes4ydq2bYv9+/dj0aJFpa6lpqbi4sWL2LBhgybsOnLkSIXeT3lUKhVatGiBY8eOAQBCQkLw+eefIysrSzNa6ujRozAzM0OzZs30voaHh4fOelpqtRpxcXE6bSwtLct9/46OjvD19cWRI0fw+OOPa+qPHTuGzp07V/n9VQeGUkRERHVJx46iyCQJuHNHjKj66y+xc6Ds1Cng7FlRtDk4iJDq0CExvRAQC57a2YnF3ImIiIi0/Pjjj3jw4AGmTJkCJycnnWsjR47Exo0bKxxKNWnSBN9++y0GDx4MlUqFN998s0IjcZ5//nkMGjQIRUVFmDBhgs61oKAgnDhxAjdv3oSDgwNcXV1LPX/evHlo06YNpk+fjmnTpsHKygoHDhzA008/DVdXV7i5ueGTTz6Bj48P4uPjMXfu3Aq9H9nZs2exYMECjBs3DiEhIbCyssLBgwexadMmzJkzBwDw7LPPYsGCBZgwYQIWLlyIe/fu4eWXX8a4cePKXE+qV69e2Lx5MwYPHgwXFxe8+eabMC8xci4oKAj79+9HREQErK2tdUatyWbNmoUFCxagcePGaNeuHaKionD27Fls3bq1Uu+zujGUIiIiqstUKqBhQ1FK+u9/gXPndEdVXbokpgfcuaMEUgAwZIgIr+TRVG3aAKGh4rG8hVeJiIjI5G3cuBG9e/cuFUgBYqTUu+++izNnzlTotVauXInJkycjPDwc7u7umDNnDtRq9UOf17t3b/j4+KBVq1bw9fXVufbaa69hwoQJCAkJQU5OTqmRRADQrFkz/Pzzz3j99dfRuXNn2NraokuXLhgzZgzMzMzw1VdfYcaMGWjdujWaN2+ONWvW4AntnZUfws/PD0FBQVi0aBFu3rwJlUqlOX/llVcAAHZ2dti7dy/+/e9/o1OnTrCzs8OIESPwwQcflPm68+bNw40bNzBo0CA4OTnh7bffLvX+VqxYgcjISHz66ado2LCh3pFnM2bMgFqtxquvvork5GSEhIRg165daKq9TIQRqCR9+zfWcevWrcP777+PxMREtGrVCqtWrSp3vunWrVuxbNkyXL16FU5OTnjqqaewfPlyuLm5Veh+arUaTk5OSE9Ph2PJ3ZeIiIhqk4IC4OpVsQuP1vBtNGwogqqSVCoxXfD4caUuJQVwc+OoKiIioirIzc1FXFwcgoODYWNjY+zu1BnZ2dnw9fXFpk2b8I9//MPY3SGU/3e5ojmJyS0osX37dsycORPz589HbGwsunfvjv79+5e5Yv6RI0cwfvx4TJkyBefPn8eOHTtw8uRJPP/88wbuORERkQFYWordALUDKQC4dg2IjRWjq2bPBvr3B3x8xPRAOzvdtmFhYt2rHj3EGlcbN4qpgtq7BBIRERFVg+LiYty5cwdvvvkmnJycMGTIEGN3iaqRyU3f++CDDzBlyhRNqLRq1Srs3bsX69evx9KlS0u1P378OIKCgjBjxgwAQHBwMF588UUsW7bMoP0mIiIyKltboF07UbTduycWUpdlZgKJiUB+vliT6tAh5ZqZGTBqFLBtm+7z3d05qoqIiIiqJD4+HsHBwfDz88PmzZthYWFyMUa9ZlKfZn5+Pk6fPl1qQbK+fftqVrsvKTw8HPPnz8fu3bvRv39/JCcn4+uvv8bAgQPLvE9eXh7y8vI05xWZ/0pERFQneXiIInNwADIyxG5/v/+uW1JSAO3h2bm5YrSVi4tYn0q7tGypu6YVERERkR5BQUEwwVWH6G8mFUqlpKSgqKio1Kr1Xl5eSEpK0vuc8PBwbN26FaNHj0Zubi4KCwsxZMgQfPjhh2XeZ+nSpXq3kSQiIqoXrKyUcEkmSWIEVWGhUnftmqhPSQH27xdFZmkJvPoqII9iLioC7t/XDcCIiIiIyKSZ3JpSAKAqMUVAkqRSdbILFy5gxowZeOutt3D69Gns2bMHcXFxmDZtWpmvP2/ePKSnp2vKrVu3qrX/REREdY5KBfj6AgEBSl3r1mK638mTwGefAS+/LNaycnISC65rb9d89Srg6SkWXB8wAHjjDeDbb4G//hLBFhERkYnh6B+q66rj77BJjZRyd3eHubl5qVFRycnJpUZPyZYuXYqIiAjMmjULANC2bVvY29uje/fuWLJkCXx8fEo9x9raGtbW1tX/BoiIiEyNra1YGD0sTKmTJBE2aS+gfvWqeLxzR5T//U+55uoKLF8OTJokzouKRAhmZpK/WyMiIhNnbm4OQCw/Y2tra+TeEFVddnY2AMDS0rLKr2FSoZSVlRU6duyI6OhoDB8+XFMfHR2NoUOH6n1OdnZ2qYXS5P9JMLkmIiKqASoVEBSkWzd4MKBWA+fOiV0AY2OBM2eAP/8U0/pcXJS2e/cCzzwDtG8PdOwIdOggSvPmwN//hhMREdVWFhYWsLOzw71792BpaQkz/pKF6hhJkpCdnY3k5GQ4OztrMpSqMKlQCgAiIyMxbtw4hIWFoVu3bvjkk08QHx+vmY43b9483L59G1u2bAEADB48GFOnTsX69evRr18/JCYmYubMmejcuTN8fX2N+VaIiIjqlwYNgPBwUWR5ecD580DjxkrdmTNisfWSu//Z2Yl1rlauBLp0MVy/iYiIKkGlUsHHxwdxcXH466+/jN0doipzdnaGt7f3I72GyYVSo0ePRmpqKhYvXozExES0bt0au3fvRmBgIAAgMTER8fHxmvYTJ05ERkYG1q5di1dffRXOzs7o1asX3nvvPWO9BSIiIpJZW4tRUNrmzgWGDhXhlFxiY4GsLCAmBrC3V9p+/DGwcaMymqpDB6BNG8DGxrDvg4iISIuVlRWaNm2K/Px8Y3eFqEosLS0faYSUTCVxjtojU6vVcHJyQnp6Ohy1t8ImIiIiwygqErv9nT4NjBoFyFPzJ04EPv9ct625OdCqlQioli4FHvE3fERERESkq6I5CUOpasBQioiIqJaKjwd++00ZUXX6NJCSIq6pVGIdKwcHcf6f/4g1rDp2BDp1EmtWaY+6IiIiIqIKqWhOYnLT94iIiIg0AgJEGTlSnEsSkJAgAqq4OCWQAoAffwSOHgW2bhXnZmZiRFWnTqJMncqF1ImIiIiqEUdKVQOOlCIiIjIB+/aJNalOnwZOngTu3FGu+foCt28r5xs2iIXVO3UCmjUTARYRERERAeBIKSIiIqLK6d1bFNnt2yKcOnkSsLJS6iUJeOstIDlZnDs6KlP+OnUCOncWo7OIiIiIqFwcKVUNOFKKiIioHsnLEzsAnjwppgHm5Ohe794dOHRIOT9wAGjdGvDwMGw/iYiIiIyEI6WIiIiIaoK1NbBypTguLAQuXBCLqcujqsLDlbbp6UCvXuI4MFAZTdWpkxhdxV9mERERUT3GkVLVgCOliIiISK+LF4F//AO4fFlM+9OmUgFz5gBLl4rz4mIgPx+wsTF8P4mIiIiqEUdKERERERlby5YimFKrlQXU5VFV8fG6a0/98YdYjyo0FOjaVSmNGokAi4iIiMjEcKRUNeBIKSIiIqq05GSxgLqzsziPigImTy7dzt1dhFOzZ4v1qoiIiIhquYrmJNy/mIiIiMgYPD2VQAoAJk4E4uKAr74CZs4UQZSVFZCSAvz4o+6C6r/8AkydCmzcCJw/L6b+EREREdUxnL5HREREVBuoVEBQkCijR4u6vDzg7Fng+HGgSxel7d69wGefiQKIBdM7d1am/D3xBGBvb9j+ExEREVUSp+9VA07fIyIiIoM6cgT46ScRVp08CWRl6V6/dg1o3Fgcnz0rRlK1aQNYWhq8q0RERFT/cKFzIiIiIlP12GOiAEBhoZjCd/y4KJcvi8XRZe+8A3z9NWBrC4SF6S6i7utrnP4TERERgaEUERERUd1mYSF27AsNBV58sfR1e3uxdlVaGnD4sCiyxo1FiGVuLs6LiwEzLjlKREREhsFQioiIiMiUbd4swqYrV5TRVMePA+fOAW5uSiAFAOHhom1EhFJ8fIzWdSIiIjJtXFOqGnBNKSIiIqpzMjOBpCSgSRNxnpUFODkBRUW67YKCRDg1cCAwZozBu0lERER1D9eUIiIiIqKyOTgogRQA2NkBV68Cx46JcvQo8McfwM2bohQVKaFUcTHw3ntix78uXcRrEREREVUSQykiIiIiAlQqIDhYlGefFXVqtZjqd+wY0KGD0vbyZeD118WxublYzyoiQkz/i4gA/P0N338iIiKqczh9rxpw+h4RERHVKxcuAEuWiNFU8fGlr7/zjhJaFRaKRwv+LpSIiKi+4PQ9IiIiIqoZISHAl1+K44QEEU7J5fffxcgp2c8/A6NHi2l+8miqrl3F+lVERERUrzGUIiIiIqKq8/MTodPo0eI8MxOwtFSunzgh6vbvFwUQUwXbtBEB1auv6q5tRURERPUGp+9VA07fIyIiIipDUZGY7iePpDp2DLhxQ7l+/rwYeQUAe/aI9aq6dxejrczNjdNnIiIieiScvkdERERExmduLkZFtWkDTJsm6hITRTh18iTQooXS9vPPga++EseOjmIkVffuwOOPA506AdbWhu8/ERER1RiOlKoGHClFREREVA02bAC+/16MqFKrda/Z2wP37gG2tuK8qIgjqYiIiGopjpQiIiIiorrlxRdFKSoCzp0DDh0CDh8WpWFDJZACgCeeAHJyxCiq7t2Bxx4DPDyM1nUiIiKqPI6UqgYcKUVERERUgyQJePAAcHUV5zk5Yve+ggLddi1bioCqf39g2DCDd5OIiIgEjpQiIiIiItOgUimBFCBGTN24oYyiOnwY+PNP4OJFUVJSlFBKksRaVV26iPWrVCqjvAUiIiIqjSOlqgFHShEREREZWWqqWIvq8GGxKPqoUaL+2jWgaVNx7OEhpvnJi6eHhgIW/B0tERFRdatoTmJmwD6VKSgoCIsXL0Z8fHy1vN66desQHBwMGxsbdOzYEYcPHy63fV5eHubPn4/AwEBYW1ujcePG2LRpU7X0hYiIiIgMwM0NGDIEeP99JZACgIwMoGdPwMZGLJS+cycQGQmEhQEuLmJxdSIiIjKKWhFKvfrqq/j+++/RqFEj9OnTB1999RXy8vKq9Frbt2/HzJkzMX/+fMTGxqJ79+7o379/uYHXqFGjsH//fmzcuBGXL1/Gtm3b0EJ7e2IiIiIiqpvatwd++QVITweOHQPeew8YOFCsSZWZCXh7K21//VWMoHrrLfGcnByjdZuIiKg+qFXT937//Xds2rQJ27ZtQ2FhIcaOHYvJkyejQ4cOFX6NLl26oEOHDli/fr2mrmXLlhg2bBiWLl1aqv2ePXvwzDPP4MaNG3DVXqugEjh9j4iIiKiOKSoS61A1agQ0aCDqFiwAFi9W2lhZAZ07i53+nngCiIgQI66IiIioXHVq+p4sNDQUq1evxu3bt7FgwQJ89tln6NSpE0JDQ7Fp0yY8LD/Lz8/H6dOn0bdvX536vn374tixY3qfs2vXLoSFhWHZsmVo2LAhmjVrhtdeew05/M0YERERkekyNxdrSsmBFABMngx8+inw7LNAw4ZAfj5w5AiwZAnQuzdw6ZLSNikJyMoyfL+JiIhMSK1a2bGgoAA7d+5EVFQUoqOj0bVrV0yZMgV37tzB/PnzsW/fPnz55ZdlPj8lJQVFRUXw8vLSqffy8kJSUpLe59y4cQNHjhyBjY0Ndu7ciZSUFEyfPh33798vc12pvLw8nemFarW6Cu+WiIiIiGqVwEDg+edFkSSxw9+vv4py9izQpo3Sdu5cYOtW3ZFU4eGAvb1Ruk5ERFQX1YpQ6syZM4iKisK2bdtgbm6OcePGYeXKlTrrOvXt2xePP/54hV5PVWKrX0mSStXJiouLoVKpsHXrVjg5OQEAPvjgA4wcORIfffQRbG1tSz1n6dKlWLRoUUXfHhERERHVNSoV0LixKFOmlL5+7RpQWCjWqTp2DHj3XbGTX+fOYmH1t98Wr0FERERlqhXT9zp16oSrV69i/fr1SEhIwPLly0stNB4SEoJnnnmm3Ndxd3eHubl5qVFRycnJpUZPyXx8fNCwYUNNIAWINagkSUJCQoLe58ybNw/p6emacuvWrYq8TSIiIiIyFYcPA9evA5s2AePHA/7+Ski1a5duIPXJJ8DPP4uF1YmIiEijVoyUunHjBgIDA8ttY29vj6ioqHLbWFlZoWPHjoiOjsbw4cM19dHR0Rg6dKje50RERGDHjh3IzMyEg4MDAODKlSswMzODn5+f3udYW1vD2tq63L4QERERkQlTqcQi6Y0aAZMmiel+N28CBw+KEVOy3FxgxgwgL0/Uh4XpLpz+9/dPIiKi+qhWjJTq2bMnUlNTS9WnpaWhUaNGlXqtyMhIfPbZZ9i0aRMuXryIV155BfHx8Zg2bRoAMcpp/PjxmvZjx46Fm5sbJk2ahAsXLuDQoUOYNWsWJk+erHfqHhERERFRKSoVEBwMTJwIPPecUq9WA2PGAEFBYiTV8ePAf/4DPPUU4OwMvPaakTpMRERkfLVipNTNmzdRVFRUqj4vLw+3b9+u1GuNHj0aqampWLx4MRITE9G6dWvs3r1bMxIrMTER8fHxmvYODg6Ijo7Gyy+/jLCwMLi5uWHUqFFYsmTJo70pIiIiIiJPT0Ae7S+PpDp4UCyeHhcH+PgobRMSgFGjgF69ROnWDeAvSYmIyISpJEmSjHXzXbt2AQCGDRuGzz//XGddp6KiIuzfvx/R0dG4fPmysbpYIWq1Gk5O/8/efYdHUe1/HP9seg81CSUkoTelSgAFRJogiBWuDVAs2LjIVQH1Ct6fytVrRQUroCKIiAUQEVDpTSAgUhUCoYUQShIS0uf3x5hNlhRSNrsp79fzzJPZM2c332XIMnxyzplAJSQkKCAgwNnlAAAAoDI4ckTy8ZHq1jUff/aZNHJk7nFPT/OOfjkh1VVXSe7uzqkVAIASKG5O4tRQysXFnD1osVh0aRnu7u4KDw/X66+/rsGDBzujvGIjlAIAAECZnTwpLVsm/fKLuZ04YXt8/nxzJJUkpaSYoZWrq+PrBADgMipFKJUjIiJCv/32m+rUqePsUkqFUAoAAAB2ZRjSgQO5AdWqVdLu3eZ0QEl66SXp9dfNBdNzRlK1amV71z8AAJykUoVSlR2hFAAAAMqVYdgGTjfcIC1datsnJETq3dsMqO6+W/LycmyNAAD8rcKHUtOmTdODDz4oLy8vTZs2rci+Y8eOdVBVpUMoBQAAAIfKzJS2bcsdSbVunZSaah7z85POns1df2rLFqlhQ6l+fefVCwCoVip8KBUREaGtW7eqdu3aioiIKLSfxWLRoUOHHFhZyRFKAQAAwKnS0qRNm8yAKjVVeuWV3GPNm0t//im1bJk71e/aa6XatZ1WLgCgaqvwoVRVQigFAACACik52Qygtm0zpwDm1b69dOed0lNPOaMyAEAVVtycxMWBNQEAAABwJF9f6bffpDNnpO++k8aOldq2NY/t2CEdPJjbNzNT+s9/zKmAGRnOqBYAUM1UiJFSt912mzp37qyJEyfatP/vf//Tli1btGDBAidVVjyMlAIAAEClcuqUeUe/xo2lq64y2zZulLp3N/f9/KRevaS+fc2tTRvu7AcAKLZKNVJq9erVuuGGG/K1X3/99VqzZo0TKgIAAACqsOBgafjw3EBKMu/W949/SHXrShcuSD/8ID3xhHTFFVK9etK33zqvXgBAlVQhQqkLFy7Iw8MjX7u7u7sSExOdUBEAAABQzXToIM2bJ8XGmlP7XntNuv56ydvbHFkVEpLbd8UK6bHHzCmB5887qWAAQGVXIUKptm3bav78+fnav/zyS7Vu3doJFQEAAADVlIuL1K6d9K9/ST/+KJ07J/36q+2oqq+/lt57T7r5ZvMufl27Ss89Z04JTEtzWukAgMrFzdkFSNK///1v3XrrrTp48KCuu+46SdLPP/+sefPmVfj1pAAAAIAqzdPTvINfXsOGSR4e0sqV0r590ubN5vbSS5KPj3TkiFSnjlPKBQBUHhVioXNJ+uGHH/Tyyy9rx44d8vb21pVXXqnJkyerV69ezi7tsljoHAAAANXWsWPSzz+bU/pWrpQCA6X9+3OPjxolpabmLpoeHu6sSgEADlLcnKTChFKVGaEUAAAAIMkwpLg4cyF1ScrIkGrVMhdOz9GkSW5A1bu3Of0PAFClVMpQatu2bdq7d68sFotat26tDh06OLukYiGUAgAAAAqQlSVt3Jg7imrzZrMtx7XXmutV5cjMlNwqxAojAIAyKG5OUiE+8ePi4vSPf/xDq1atUo0aNWQYhhISEtS7d299+eWXqlu3rrNLBAAAAFBSrq7SNdeY2wsvSImJ0po1ZkC1cqXUv39u39OnpaZNpV69zPb+/aVmzSSLxXn1AwDKVYUYKTV8+HAdPHhQn3/+uVq1aiVJ2rNnj0aOHKmmTZtq3rx5Tq6waIyUAgAAAEohO9u8258kffWVNHy47fFGjXIDqr59pZo1HV8jAKDEKtX0vcDAQK1cuVJX5b3NrKQtW7aof//+On/+vHMKKyZCKQAAAKCMsrOlnTul5cvNbd06KT099/isWeai6ZKUnGze/c/d3SmlAgCKVtycxMWBNRUqOztb7gX8g+Lu7q7s7GwnVAQAAADAoVxcpA4dpAkTzLv5nT0r/fij9MQTUuvWUr9+uX0/+MBcQH3oUOm996Q//zQXWQcAVCoVYqTU0KFDdf78ec2bN0/169eXJB0/flx33XWXatasqW+//dbJFRaNkVIAAACAA91+u/T117ZtYWG5U/2GDJE8PZ1TGwCgck3fO3r0qIYOHao//vhDoaGhslgsiomJ0RVXXKHvv/9eDRs2dHaJRSKUAgAAABwoO1vasSN3qt/69blT/Tw9pXPnJG9v8/GRI1L9+kz1AwAHqlShVI4VK1Zo3759MgxDrVu3Vt++fZ1dUrEQSgEAAABOlJxs3tVv+XLp4kXp/fdzj7VrJ0VHS9ddlzuSqkkT7uoHAOWoUoZSlRWhFAAAAFABJSWZAdTp07btERHSgAHSzTebIRUAwK6Km5O4ObAmG9OmTSt237Fjx5ZjJQAAAACqJH9/KTZWioqyneoXHW2OpkpJyQ2lcu7+166dueg6AKDcOW2kVERERLH6WSwWHTp0qJyrKRtGSgEAAACVxIUL0qpV0k8/SQMHSoMGme07dph3/wsKMkdRDRhgBlZ16zqzWgColJi+50CEUgAAAEAlt2CBdO+95vpUOSwWqVMnM6C6915zKiAA4LKKm5NUqHGp6enp2r9/vzIzM51dCgAAAIDq5PbbpbNnpV9/lSZMkNq3lwxD2rpVeukl8y5+OWJibB8DAEqlQoRSKSkpGj16tHx8fNSmTRvFxMRIMteS+u9//+vk6gAAAABUCx4e0rXXSv/9r7kO1cmT0qefSvfcI119dW6/N96QwsOlVq2kceOkZcvMu/4BAEqkQoRSkyZN0s6dO7Vq1Sp5eXlZ2/v27av58+c7sTIAAAAA1VZIiDRihPTZZ5KnZ277mTPmYuj79klvv22uTVWzpjnN7403pIwM59UMAJVIhQilvvvuO7377ru65pprZLFYrO2tW7fWwYMHS/x606dPV0REhLy8vNSpUyetXbu2WM9bv3693Nzc1L59+xJ/TwAAAADVxOefS/Hx5jpU998vNWwopaWZd/d76y3JLc9Nzjdvls6fd1alAFChuV2+S/k7ffq0goKC8rUnJyfbhFTFMX/+fI0bN07Tp0/X1VdfrQ8++EADBw7Unj171KhRo0Kfl5CQoBEjRqhPnz46depUid8DAAAAgGqkZk3pttvMzTCkvXvNaXxubuYC6ZKUlWWOokpMlLp2NfcHDjTXq3KpEOMDAMCpKsQn4VVXXaUffvjB+jgniProo4/UrVu3Er3WG2+8odGjR+v+++9Xq1at9NZbbyk0NFQzZswo8nkPPfSQ7rzzzhJ/PwAAAADVnMUitW4tjR8vjR2b237ihBQcbIZT69dLzz1n3s2vfn1p1Chp5UqnlQwAFYFTR0rt2LFD7du313//+18NGDBAe/bsUWZmpt5++23t3r1bGzdu1OrVq4v9eunp6dq2bZsmTpxo096/f39t2LCh0OfNmjVLBw8e1Jw5c/Tiiy9e9vukpaUpLS3N+jgxMbHYNQIAAACoJkJDzRFUhw+bo6h+/FH6+Wfp1ClzAfXQUKlvX7NvcrK5RlWHDoyiAlBtOPXTrmPHjurUqZN27NihpUuXKiUlRU2aNNHy5csVHBysjRs3qlOnTsV+vfj4eGVlZSk4ONimPTg4WLGxsQU+588//9TEiRP1xRdfyM2teBnd1KlTFRgYaN1CQ0OLXSMAAACAaiY8XBozRvr+e3OR9JUrpX/9S7rlltw+K1dKnTubo6hGjpS+/FI6e9ZpJQOAIzh1pNT69es1c+ZMTZw4URkZGbrllls0bdo0XXfddWV63UvXoTIMo8C1qbKysnTnnXfqhRdeUPPmzYv9+pMmTdL48eOtjxMTEwmmAAAAAFyep6fUp4+55XXihOTnZ46i+uwzc3NxkSIjzXWoHnjAvBsgAFQhFsMwDGcXcfHiRX311VeaNWuW1q5dq/DwcN13330aOXKkGjZsWOzXSU9Pl4+PjxYsWKCbb77Z2v7Pf/5TO3bsyDcV8Pz586pZs6ZcXV2tbdnZ2TIMQ66urlq+fHmxArLExEQFBgYqISFBAQEBxa4XAAAAAKzS06V168xpfj/+KO3enXvsr7+kJk3M/YMHpRo1pNq1nVImAFxOcXOSChFK5XXw4EHNmjVLn332mU6ePKl+/fpp6dKlxX5+ZGSkOnXqpOnTp1vbWrduraFDh2rq1Kk2fbOzs7Vnzx6btunTp+uXX37R119/rYiICPn6+l72exJKAQAAALC7mBhzLaqoKCnvjZtuvllatEjq0iX3jn6dOrEWFYAKo7g5iVOn7xWkSZMmmjhxokJDQ/XMM8/op59+KtHzx48fr3vuuUedO3dWt27d9OGHHyomJkZjxoyRZE69O378uD777DO5uLiobdu2Ns8PCgqSl5dXvnYAAAAAcKhGjaQHH7RtMwwpLk7KzpY2bTK3yZOlunWlAQOkIUOkYcOcUy8AlFCFCqVWr16tmTNnauHChXJ1ddWwYcM0evToEr3G8OHDdebMGf3nP//RyZMn1bZtWy1dulRhYWGSpJMnTyomJqY8ygcAAOXEMMw7qmdmml9ztqIel/ZYdnbBm2EUr62sffOOYS/LfmmfI5l3t8/ZXFxsHxfVXty2ovrmbK6u5laS/dI+L+++m1vRGwNR4HQWi7R+vXT0aO4d/VaulE6flubMkaKjbUOpffuk5s35ywugQnL69L2jR49q9uzZmj17tqKjo9W9e3eNHj1aw4YNK9bUuYqA6XsAgIooK8tcniTvlpZWvLb0dCkjwwxrMjLy75fnsZwtb2BUsRYbQHXm4nL54Crv5u5esr7u7pKHR+FfizpWmq9ubmbGgUouPV3asMEMqVq0kO6912w/c0YKCjK3gQOlQYOkfv2kwEDn1gugyqsUa0r169dPv/76q+rWrasRI0bovvvuU4sWLZxVTqkRSgEADMMMd1JTc7/m3S9NW2GhUXGDpawsZ/+pOIbFkjvCJWfUy6WPS3Is76ibnNE8eUfwFNRWnD7FeV7O40vfX2n3S/Mcwyh4yxnFVZJjpW3PO2qtNPulfV7eIDQzs/h/Byu7nLDLw8O8MVxxt5L0L6yvl1f+Lc89iFBWa9aYQVRycm6bm5t0zTVm+223SRERzqsPQJVVKdaU8vb21sKFCzV48GCbO+ABAFBa2dlmoHPxon22nIDocmFSerqz3/nlubnl/scw739C8/5ntKBRFDmjNxz1OGcrbpjEKA+Uh5yQ7NIRfMXZSvucnC1npGJZvhZ2rKCwLad/ReHuboZT3t62YVXex2U95u1tbj4+5ubtbX6mVDk9e5qjpdatk374QVq6VNq/X1q1ytxq1pTuv9/sm5RkpuKVZLYKgKrB6dP3qgJGSgHA5eWERcnJUkqKueXsF9RW2P7lQqS0NGe/U1POf4DyjgTI2S9OW87jwoKjkra7u7OcCADzszgzM3+AlTPiMme79PHlttL2zwn4K8LINHf3/EHVpftlafPxMfMeT08nh+kHD5rrUP3wg/TRR1LDhmb7tGnS009L114r3XCDOZKqSRMnFgqgMqsU0/eqCkIpAFVFZqYZ/ly4YG5F7edsxQmSkpPNwMjR3Nxyfxtelq2kAZO7O6N3AKAkMjNzQ6q8o1QL2y/tsbyjYHN+0eFoOYORckKqwraijhd1rNQTUEaMkD7/3LateXMznLrhBqlXL/MfOAAoBkIpByKUAuBohmFeSCcl5W5FhUiXC5hy9h01ysjLK/eCOu9vjy/dz9uW9zfOxd2q5FQMAIDdGEZuWJXzC5Wc/eK2Fec5ycnmyDRH8PQ0//308yt68/e/pM3XUNDZfWqw4wfV3rJUvtvXyvL3EDbDw0OWM2fMjpL5pry9HfOGAFRKlWJNKQCoTtLSbEOkS7cLF4o+fmnf8lzE2tXV9kI178Vtzn7e39YWJ1TK2ff2ZhFbAEDFYLHk/iKjVq3y/V45o5HzjiIubCvqeGHHcoYa5EyRPHu2pBVaJLX6e3tS/kpUP63QIC2VV0a6Hgv1s14LfBtztdwtWdpe7wbtCR+k2PCu8g10k7+/GXYFBKjIfU9Pu/7RAqjEGCllB4yUAqouwzAv9BITzS0hIXe/sO3SPjlBUnn9hjTvbztzvhYWIhUVMuXd9/Bg+hkAAJVFzoivnNCqoBHTOVvOL7cK2/IeT03N/71q6YxOKVhuyv3t2FnV1DJdrx90g5bpep1V7SLrdXcvOrwq7FhgoLmf8zUggBmFQEXF9D0HIpQCKqb0dDMgSkiQzp/Pv1/cQCk72751+fjkBkhl2XJCJBavBgAA5eHStSZzQqu04/EK2PiT6v62VA3+WCbvlNxhWevD7tR/r/jC/KVcoqGkJCkxyaKkJDMwszdv79yAKm9YVVCAVdh+QACjuAF7I5RyIEIpwP6ysnJDooICpaLCppz9gn67V1quroVfxOTdLj126W/6/Py46AEAAFVIZqa0ebN5N78lS6RJk6Q77jCP7dplLpL+95bZ8zpdyPaxWZIg76jyoh5f+ktEewdcvr7mdVyNGrZfi9vm58cocyAvQikHIpQC8suZ9nb+vHTunPk17/7l2hIT7VeLn1/+C4mcraiQKW+7tzcXGgAAAJdlGLkXTa+8Ik2cmHvMy0vq3VsaPNgMqsLCSv1tMjPNsCrvKPeC9i933F6/xHRxyR9Y5d2vWdPcr1Ejdz9vm78/o99RtRBKORChFKoqwzD/sT571gyMzp3Lv19UsPT3DVvKxMur6H/gL3csIIA7sAEAADjFxYvSr7/mjqKKibE9vmaN1KOHc2r7W3p6bkh16ej7S78Wdswe17w5odblwqtL22rVMvc9PMpeA2BPhFIORCiFiswwzOuBgoKly7WdO1f29ZTc3Ar+h/Ry+znhEndnAQAAqAIMQ9q9Ozeg2rVLOnUq92Lv//5P2rvXHEF1/fVS7aIXS68ocq61LxdcFfaL3HPnzGCsrHx8cgOqnC3v48KO1ajBL3BRPgilHIhQCo6SEy6dOWN+zbtfUFvOflpa2b6vl1fuP1yX/oOWsxUWLvn4MO0NAAAAl0hJMS8Uc7RsKe3fb+67uEjduuWuR3XFFVX6gjIn1Crtshdl/R99QEDudX5RW+3ato/55TGKQijlQIRSKKmsLPMfkvh4MzTKu+W0FRQulWXOe86IpbzBUkG/PSmozcvLfu8dAAAAsGEY0oYN5giqH34wR1Hl1bWrtHGjc2qr4LKzzdFYBc14KGoJjnPnzDW5yiJndFZhAVbOduljd3f7vHdUbIRSDkQoVb2lp+eGSXlDpksDp7yPy/IbDTe3wn9jUdB+7dpmsOTvX6V/wQQAAICqIibGDKd++EH6+Wfp7ruljz4yj2VnSyNGSL16maOo6td3bq2VWGam+f+SvMt4FHcryxIf/v5Fh1Y5W506uV+5u2HlQyjlQIRSVUdWlvkhmxMwFWcry13iAgNtP3AL2i4NmQiXAAAAUG2kpJhDeoKDzcebNplT+3J07GjezW/IEHOfW9iVu+xs85TkndWRd8v5RXze/TNnzOCrtOmDu7ttSJXztbC2OnX4f5OzEUo5EKFUxXXxonT6tLnFx+fuX/o4Z7+0H5QuLgUn+kUl/rVqsaggAAAAUCLHjkmffmpO9du82fbiPSREeucd6bbbnFcfCpWVZY7MKiy0KmiLjy/9EiY5QVadOlLduraBVd4t51jduqyTZU+EUg5EKOU4yclSXFxumJR3/9LH8fFm/9KoWbPwD62Ctho1+KUMAAAA4FCnTkk//mgGVD/9JF24IK1dK11zjXl8yxbpt9/MkVRhYc6tFaWWkmK7VEpRX3P2U1JK9738/GxDqqL269Y1F4lnNFbBCKUciFCq9FJTbcOkuLj8W97jFy+W/Hu4u1/+AyVvQl67NiOYAAAAgEolLc0MpHr3llxdzbZHHpFmzDD3r7jCDKcGD5YiI3P7oEpKSbENqnIGLRS05RzLzCz59/HwyB9U5WxBQfm/BgZWnxC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      "text/plain": [
       "<Figure size 1200x800 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Maximum residual: 2.65e-02\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "from numpy.polynomial.chebyshev import Chebyshev\n",
    "from scipy.optimize import least_squares\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# 定义问题参数\n",
    "t0 = 0.0       # 初始时间\n",
    "tf = np.pi/2   # 终止时间\n",
    "y0 = 0.0       # 初始位置\n",
    "dy0 = 1.0      # 初始速度\n",
    "yf = 1.0       # 终止位置\n",
    "dyf = 0.0      # 终止速度\n",
    "\n",
    "# Chebyshev多项式阶数\n",
    "m = 6          # 基函数个数\n",
    "N = 50         # 离散点数量\n",
    "\n",
    "# 时间离散化（Chebyshev配点）\n",
    "z = -np.cos(np.linspace(0, np.pi, N))  # z ∈ [-1, 1]\n",
    "t = t0 + (tf - t0)/2 * (z + 1)        # 映射到 [t0, tf]\n",
    "\n",
    "# 定义基函数（Chebyshev多项式）及其导数\n",
    "def get_basis(n, t_range, m):\n",
    "    scaled_t = 2*(t - t_range[0])/(t_range[1] - t_range[0]) - 1\n",
    "    basis = [Chebyshev.basis(i)(scaled_t) for i in range(m)]\n",
    "    dbasis = [Chebyshev.basis(i).deriv()(scaled_t) * 2/(t_range[1]-t_range[0]) for i in range(m)]\n",
    "    ddbasis = [Chebyshev.basis(i).deriv(2)(scaled_t) * (2/(t_range[1]-t_range[0]))**2 for i in range(m)]\n",
    "    return np.array(basis), np.array(dbasis), np.array(ddbasis)\n",
    "\n",
    "# 构造约束表达式\n",
    "def constrained_expression(g, dg, ddg, t, t0, tf):\n",
    "    dt = tf - t0\n",
    "    t_ = t - t0\n",
    "    \n",
    "    # 定义Omega函数（来自论文表I）\n",
    "    Omega1 = (2*t_**3)/(3*dt**2) - t_**2/dt + t_\n",
    "    Omega2 = -(2*t_**3)/(3*dt**2) + t_**2/dt\n",
    "    Omega3 = t_**3/(3*dt) - t_**2/2\n",
    "    Omega4 = t_**3/(3*dt) - t_**2/2 + t_*dt/6\n",
    "    \n",
    "    # 构造约束表达式及其导数\n",
    "    y = g + Omega1*(y0 - g[0]) + Omega2*(yf - g[-1]) + Omega3*(dy0 - dg[0]) + Omega4*(dyf - dg[-1])\n",
    "    dy = dg + (6*t_**2/(3*dt**2) - 2*t_/dt + 1)*(y0 - g[0]) + \\\n",
    "         (-6*t_**2/(3*dt**2) + 2*t_/dt)*(yf - g[-1]) + \\\n",
    "         (3*t_**2/(3*dt) - t_)*(dy0 - dg[0]) + \\\n",
    "         (3*t_**2/(3*dt) - t_ + dt/6)*(dyf - dg[-1])\n",
    "    \n",
    "    ddy = ddg + (12*t_/(3*dt**2) - 2/dt)*(y0 - g[0]) + \\\n",
    "          (-12*t_/(3*dt**2) + 2/dt)*(yf - g[-1]) + \\\n",
    "          (6*t_/(3*dt) - 1)*(dy0 - dg[0]) + \\\n",
    "          (6*t_/(3*dt) - 1)*(dyf - dg[-1])\n",
    "    \n",
    "    return y, dy, ddy\n",
    "\n",
    "# 定义微分方程残差（示例方程：y'' + y = 0，真实解为y=sin(t)）\n",
    "def residuals(xi):\n",
    "    # 将系数向量转换为矩阵\n",
    "    xi = xi.reshape((m, 1))\n",
    "    \n",
    "    # 计算基函数及其导数\n",
    "    basis, dbasis, ddbasis = get_basis(m, (t0, tf), m)\n",
    "    \n",
    "    # 自由函数及其导数\n",
    "    g = xi.T @ basis\n",
    "    dg = xi.T @ dbasis\n",
    "    ddg = xi.T @ ddbasis\n",
    "    \n",
    "    # 构造约束表达式\n",
    "    y, dy, ddy = constrained_expression(g, dg, ddg, t, t0, tf)\n",
    "    \n",
    "    # 计算残差：y'' + y\n",
    "    residual = ddy + y\n",
    "    return residual.flatten()\n",
    "\n",
    "# 初始猜测（系数全为零）\n",
    "xi0 = np.zeros(m)\n",
    "\n",
    "# 使用最小二乘法求解\n",
    "result = least_squares(residuals, xi0, method='lm', verbose=1)\n",
    "\n",
    "# 提取最优系数\n",
    "xi_opt = result.x\n",
    "\n",
    "# 生成最终解\n",
    "basis, dbasis, ddbasis = get_basis(m, (t0, tf), m)\n",
    "g_opt = xi_opt @ basis\n",
    "dg_opt = xi_opt @ dbasis\n",
    "ddg_opt = xi_opt @ ddbasis\n",
    "\n",
    "y_tfc, dy_tfc, ddy_tfc = constrained_expression(g_opt, dg_opt, ddg_opt, t, t0, tf)\n",
    "\n",
    "# 计算真实解\n",
    "y_true = np.sin(t)\n",
    "dy_true = np.cos(t)\n",
    "ddy_true = -np.sin(t)\n",
    "\n",
    "# 绘制结果\n",
    "plt.figure(figsize=(12, 8))\n",
    "\n",
    "plt.subplot(3, 1, 1)\n",
    "plt.plot(t, y_tfc, 'b-', label='TFC Solution')\n",
    "plt.plot(t, y_true, 'r--', label='Analytical Solution')\n",
    "plt.ylabel('Position')\n",
    "plt.legend()\n",
    "\n",
    "plt.subplot(3, 1, 2)\n",
    "plt.plot(t, dy_tfc, 'b-', label='TFC Solution')\n",
    "plt.plot(t, dy_true, 'r--', label='Analytical Solution')\n",
    "plt.ylabel('Velocity')\n",
    "plt.legend()\n",
    "\n",
    "plt.subplot(3, 1, 3)\n",
    "plt.plot(t, ddy_tfc + y_tfc, 'g-', label='Residual')\n",
    "plt.axhline(0, color='k', linestyle='--')\n",
    "plt.ylabel('Residual (y\\'\\' + y)')\n",
    "plt.xlabel('Time')\n",
    "plt.legend()\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "# 输出最大残差\n",
    "print(f\"Maximum residual: {np.max(np.abs(ddy_tfc + y_tfc)):.2e}\")"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "base",
   "language": "python",
   "name": "python3"
  },
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